Dúvidas em azul eu acho que já entendi, mas deixei aqui a resposta para que a Aisha do futuro possa consultar também. Dúvidas em vermelho ainda precisam de resposta.
Resposta: * u.m.c. milhão (é a unidade que o Bacen usa para algumas variáveis) * variação % mensal (tipo quando pega o PIB e calcula o de hoje menos o de ontem dividido pelo de ontem) * IPCA - price index ou inflation rate ? * BM&FBOVESPA S.A. - Bolsa de Valores, Mercadorias e Futuros (BM&FBOVESPA) * Capital income * Labor income * Capital-Labor ratio * Interest rate (o que fazer com SELIC, deixo SELIC mesmo?) * 3 month treasury bill rate * Price index ou Inflation rate? * Real Effective Interest Rate Index (Índice da Taxa de Câmbio Efetiva Real) * Precisa traduzir as fontes dos dados? Por exemplo, Banco Central departamento de estatísticas ou a Bovespa?
Resposta: Isso também. Mas o fato de usar um passeio aleatório como lei de movimento dos coeficientes naturalmente impõe uma estrutura não estacionária no modelo.
\[y_t = c_t + B_{1,t}\cdot y_{t-1} + \ldots + B_{p,t} \cdot y_{t-p} + A_t^{-1} \cdot \Sigma_t\cdot \varepsilon_t\] (a especificação completa pode ser vista aqui).
Na prática o que o algoritmo faz é calcular a FIR para cada uma das estimativas obtidas pelo algoritmo MCMC e então calcula a média e os quantis desses valores.
Resposta:
Eu li e não achei resposta pra isso:
O pouco que eu acho que entendi é que a função por default usa um critério (baseado na verossimilhança) para definir se o modelo SARIMA ajustado é multiplicativo ou aditivo. Mas isso ainda não me ajuda a entender porque a escala da variável dessazonalizada não é em log, então alguma coisa ainda está confusa…
Resposta:
Por outro lado, se a taxa de câmbio aumenta, os investimentos em moeda estrangeiro ficam mais rentáveis e os rendimentos do capital ficariam maiores, pensando exclusivamente em capital financeiro. Mas se pensar em termos de capital físico, se uma pessoa precisa importar uma máquina de sorvete (de ANDRADE, C.R., 2018) e o câmbio aumentou, ela vai precisar gastar mais dinheiro para comprar a máquina. Por outro lado, quem exporta, vai ganhar mais. Argh. Merda de economia aberta.
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This code has all the calculations used in the work “The Impact of Monetary Policy on Income Inequality: Evidences from Brazilian Economy”. It is divided in three parts: the first one deals with data preparation and some descriptive statistics; second part estimates a VAR model and third part assess the convergence diagnostics for the MCMC algorithm.
To estimate the VAR model, I used the bvarsv do Fabian Kruger package. This two files are very helpful: bvarsv: An R implementation of the Primiceri (2005) model for macroeconomic time series and Replication of figures in Del Negro and Primiceri (2015). For the diagnostics, I used the coda package.
If mirror 10 (“UFRJ”) is offline, try changing ind = 10 to ind = 1. Do the same thing if you get an error installing the BETS package.
chooseCRANmirror(graphics = FALSE, ind = 10)
if (!require("pacman")) install.packages("pacman")
pacman::p_load(devtools, ggplot2, forecast, BETS, seasonal, seasonalview, bvarsv, lubridate, zoo, stargazer, gridExtra, reshape2, ggfortify, RColorBrewer, scales, quantmod, PerformanceAnalytics, strucchange, coda, foreach, doParallel, knitr, grid, ggpubr, gdata, vars, urca, compiler, DescTools)
These are some auxiliary functions used later in the code (I took them from bvarsv documentation):
## Some graphical parameters
matplot2 <- function(...){
matplot(..., type = 'l', lty = 1, lwd = 2, bty = "n", ylab = "")
}
# Stat.helper calculates que quantiles and organizes them in quantile 1, mean, quantile 3 given a vector z
stat.helper <- function(z) c(mean(z), quantile(z, c(0.16, 0.84)))[c(2,1,3)]
# Color palette
cbPalette <- c("#999999", "#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2", "#D55E00", "#CC79A7")
cols1 <- cbPalette[c(2,4,2)]
cols2 <- cbPalette[c(2,4,6)]
# This one is for IRF analysis
stat.helper2 <- function(z) c(mean(z), quantile(z, c(0.05, 0.25, 0.75, 0.95)))[c(2, 3, 1, 4, 5)]
All data was obtained from Brazil’s Central Bank repository (Sistema Gerenciador de Séries do Banco Central - SGS). The following series were used (obs: beginning and end of the series corresponds to the available data, not actual data used in the work and some data were manipulated, for example interest rate were converted to annual - mannipulations are described in code and in the paper appendix):
Obs: Para ver o ADF, usei isso aqui: https://stats.stackexchange.com/questions/24072/interpreting-rs-ur-df-dickey-fuller-unit-root-test-results
# Auxiliary variables, so I don't need to bother when something changes
inicio <- "1996-01-01"
fim <- "2018-02-28"
inicio_deflator <- "1993-12-31"
inicio_swap <- "1999-09-01"
# Don't mess with this code
inicio_cambio <- paste(seq(as.Date(inicio), length = 2, by = "-1 month")[2]) # 1 month before the beginning of the other series
inicio_ipca2 <- paste(seq(as.Date(inicio), length = 12, by = "-1 month")[12]) # 12 months before the beginning of the other series
fim_ipca <- paste(seq(as.Date(fim), length = 2, by = "1 month")[2]) # 1 month after the end of the other series
inicio_swap2 <- paste(seq(as.Date(inicio_swap), length = 2, by = "-1 month")[2]) # 1 1 month before the beginning of the other series
## Obs: In case you have a SQL problem, rollback this two packages and mannually download BETS from CRAN and reinstall it as well
## See: https://stackoverflow.com/questions/43073782/rmysql-system-error-10060 and https://github.com/pedrocostaferreira/BETS/issues/29
# require(devtools)
# install_version("DBI", version = "0.5", repos = "http://cran.us.r-project.org")
# install_version("RMySQL", version = "0.10.9", repos = "http://cran.us.r-project.org")
################################
##### Capital labor ratio ######
################################
trabalho <- BETS.get("7620", from = inicio, to = fim)
capital <- BETS.get("7621", from = inicio, to = fim)
capital_trabalho <- capital/trabalho
########################
##### Price Index ######
########################
ipca_raw <- BETS.get("433", from = inicio_deflator, to = fim_ipca)
ipca2 <- ipca_raw
ipca2[1] <- 100
# The following calculation was made following IPEA methodology: http://www.ipeadata.gov.br/iframe_transformacao.aspx?width=1474&height=701
# Transforms in index
for (i in 2:length(ipca2)){
ipca2[i] <- round(ipca2[(i-1)]*(1+ipca2[(i)]/100),2)
}
# Geometric Average
for (i in 1:(length(ipca2)-1)){
ipca2[i] <- sqrt(ipca2[i]*ipca2[(i+1)])
}
# Change base to mar/2018
for (i in 1:length(ipca2)) {
ipca2[i] <- tail(ipca2, n=2)[1]/ipca2[i]
}
# Elimitates data outside the period we are studying
ipca2 <- ts(ipca2, start = c(1993, 12, 31), frequency = 12)
ano_ipca <- as.numeric(substr(inicio_cambio, start = 1, stop = 4))
mes_ipca <- as.numeric(substr(inicio_cambio, start = 6, stop = 7))
ipca2 <- window(ipca2, c(ano_ipca, mes_ipca))
ano_ipca <- as.numeric(substr(inicio_ipca2, start = 1, stop = 4))
mes_ipca <- as.numeric(substr(inicio_ipca2, start = 6, stop = 7))
ipca_raw <- window(ipca_raw, c(ano_ipca, mes_ipca))
# Removes last observation
ipca_raw <- ipca_raw[1:(length(ipca_raw)-1)]
ipca_acum <- ipca_raw/100 + 1
ipca <- vector()
final <- length(ipca_acum)
for (i in 12:final){
ipca[(i-11)] <- (prod(ipca_acum[(i-11):i])-1)*100
}
ano <- as.numeric(substr(inicio, start = 1, stop = 4))
mes <- as.numeric(substr(inicio, start = 6, stop = 7))
dia <- as.numeric(substr(inicio, start = 9, stop = 10))
ipca <- ts(ipca, start = c(ano, mes, dia), frequency = 12) # Date format YYYY MM DD
################
##### GDP ######
################
PIBmensal <- BETS.get("4380", from = inicio_cambio, to = fim)
PIBmensal <- PIBmensal * ipca2
##########################
##### Exchange rate ######
##########################
# Antigo câmbio nominal
#cambio_raw <- BETS.get("3696", from = inicio_cambio, to = fim)
cambio_raw <- BETS.get("11752", from = inicio, to = fim) # Since this is already an index, I don't need to take the log-diff
###########################
##### Interest rates ######
###########################
selic_4390 <- BETS.get("4390", from = inicio, to = fim)
# Transforms into anual rate
selic <- ((1+selic_4390/100)^(12)-1)*100
swap90 <- BETS.get("7818", from = inicio_swap, to = fim)
The output of the seasonality tests will appear. The analysis is hidden inside the code.
# Calculates the structural breaks
bp_ts <- breakpoints(capital_trabalho ~ 1)
ci_ts <- confint(bp_ts)
# Monthplot aggregates days and months and takes averages
meses <- ggmonthplot(capital_trabalho) +
theme_bw() +
#scale_y_continuous(name = "Capital-Labor Ratio (% - average)") +
scale_y_continuous(name = "Razão capital-trabalho (%)") +
labs(title = "", x = "Mês", subtitle = "")+
theme(axis.title = element_text(size=7), axis.text.x = element_text(angle=25, hjust = 1, size = 7))
#labs(title = "Média diária e mensal da razão capital-trabalho", x = "Mês", subtitle = "Nenhuma transformação")
#labs(title = "Daily and monthly averages of Capital-Labor ratio", x = "Month", subtitle = "No data transformation")
# Seasonplot has the averages for month, each line represents a year
season <- ggseasonplot(capital_trabalho, year.labels = TRUE) +
geom_point() +
theme_bw() +
scale_y_continuous(name = "Razão capital-trabalho (%)") +
labs(title = "", x = "Mês", subtitle = "")+
theme(axis.title = element_text(size=7), axis.text.x = element_text(angle=25, hjust = 1, size = 7))
#scale_y_continuous(name = "Capital-Labor Ratio (% - average)") +
#labs(title = "Monthly averages of Capital-Labor ratio", x = "Months", subtitle = "No data transformation")
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Season_CT.pdf", width = 6, height = 3)
season
#dev.off()
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Month_CT.pdf", width = 6, height = 3)
meses
#dev.off()
Data <- seq(as.Date("1996-01-01"), length = length(capital_trabalho), by = "1 month")
df1 <- melt(data.frame(Data,capital_trabalho), id.vars = "Data")
names(df1) <- c("Data", "Variavel", "Valor")
# Graph with structural break (dashed) and CI (red)
p1 <- ggplot(df1[which(df1$Variavel == "capital_trabalho"),], aes(Data, Valor, colour = Variavel)) +
geom_line(alpha = 1, show.legend=F, colour = cores[1])+
scale_y_continuous(name = "Razão capital-trabalho (%)") +
#scale_y_continuous(name="Capital-Labor ratio") +
scale_x_date(date_breaks = "12 months", name = "Data", labels = date_format("%m-%Y"))+
geom_vline(xintercept = Data[bp_ts$breakpoints], linetype="longdash")+
geom_segment(aes(x = Data[ci_ts$confint[1]], y = min(capital_trabalho), xend = Data[ci_ts$confint[3]], yend = min(capital_trabalho)))+
theme_bw()
p1 <- p1 + theme(axis.text.x = element_text(angle=25, hjust = 1, size = 6), legend.position = "none")
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Quebra_CT.pdf", width = 6, height = 3)
p1
#dev.off()
# We divide the series in pieces (accordingly to the structural break)
capital_trabalho_a <- capital_trabalho[1:bp_ts$breakpoints]
capital_trabalho_b <- capital_trabalho[(bp_ts$breakpoints+1):length(capital_trabalho)]
capital_trabalho_a <- ts(capital_trabalho_a, start = c(1996, 01, 01), frequency = 12)
capital_trabalho_b <- ts(capital_trabalho_b, start = c(2004, 02, 01), frequency = 12)
m <- seas(x = capital_trabalho_a, transform.function = "none", regression.aictest = NULL)
#m <- seas(x = capital_trabalho_a, regression.aictest = NULL)
## First diagnostics is using qs() function to check for seasonality after the adjustment
qs(m)
## qs p-val
## qsori 34.12733 0.00000
## qsorievadj 91.53477 0.00000
## qsrsd 0.00000 1.00000
## qssadj 0.00000 1.00000
## qssadjevadj 0.00000 1.00000
## qsirr 0.00078 0.99961
## qsirrevadj 0.00000 1.00000
## qssori 33.13775 0.00000
## qssorievadj 85.86391 0.00000
## qssrsd 0.00000 1.00000
## qsssadj 0.00000 1.00000
## qsssadjevadj 0.00000 1.00000
## qssirr 0.05069 0.97497
## qssirrevadj 0.00000 1.00000
# Click here to see the how the qs statistics is calculated: https://stats.stackexchange.com/questions/148573/the-results-and-specifics-from-the-qs-function-in-r
# The first 7 results are related to the whole series, the last 7 comprehends only the last 8 years
# qsori is the original series
# qsorievadj is the original series corrected for extreme values
# qsrsd is the residual's series of the ARIMA model
# qssadj is the series with seasonal adjustment
# qssadjevadj is the series with seasonal adjustment corrected for extreme values
# qsirr is the series of the irregular component
# qsirrevadj is the series of the irregular component corrected for extreme values
# by the output, we can conclude that there is no evidence of seasonal components in the adjusted series, the residuals and the irregular component, even when we look just the last 8 years.
# Next step is to diagnose the pre-adjust and the ARIMA model
summary(m)
##
## Call:
## seas(x = capital_trabalho_a, transform.function = "none", regression.aictest = NULL)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## AO1996.Jan -0.35561 0.10377 -3.427 0.000611 ***
## AO1998.Jan 0.67046 0.08634 7.766 8.12e-15 ***
## LS1998.Jul 0.28775 0.05339 5.390 7.06e-08 ***
## AO1998.Aug 0.29547 0.08564 3.450 0.000561 ***
## AO1999.Feb 0.68086 0.09704 7.016 2.28e-12 ***
## AO1999.Mar 0.37531 0.09644 3.892 9.96e-05 ***
## AO2002.Oct 0.49217 0.08564 5.747 9.10e-09 ***
## AR-Nonseasonal-01 0.64477 0.07100 9.081 < 2e-16 ***
## MA-Seasonal-12 0.99965 0.08975 11.138 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## SEATS adj. ARIMA: (1 0 0)(0 1 1) Obs.: 97 Transform: none
## AICc: -109.8, BIC: -88.36 QS (no seasonality in final): 0
## Box-Ljung (no autocorr.): 20.02 Shapiro (normality): 0.9765 .
# We have an level-shift outlier in July, 1998 (Asian crisis?)
# We also have additive outliers in Jan96, Jan98, Aug98, Feb99, Mar99, Oct02
# The estimated model is an ARIMA (1 0 0)(0 1 1) with the non-seasonal AR significative and the MA seasonal significative.
capital_trabalho_2a <- final(m)
m <- seas(x = capital_trabalho_b, transform.function = "none", regression.aictest = NULL)
#m <- seas(x = capital_trabalho_b, regression.aictest = NULL) # se tomar o log, fica melhor
qs(m)
## qs p-val
## qsori 242.32197 0.00000
## qsorievadj 287.80760 0.00000
## qsrsd 0.00000 1.00000
## qssadj 13.25076 0.00133
## qssadjevadj 0.00000 1.00000
## qsirr 6.90372 0.03169
## qsirrevadj 0.00000 1.00000
## qssori 134.89609 0.00000
## qssorievadj 155.37794 0.00000
## qssrsd 4.35854 0.11312
## qsssadj 5.14745 0.07625
## qsssadjevadj 0.00000 1.00000
## qssirr 7.59824 0.02239
## qssirrevadj 0.00000 1.00000
summary(m)
##
## Call:
## seas(x = capital_trabalho_b, transform.function = "none", regression.aictest = NULL)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## AO2004.Jun -0.74155 0.05278 -14.049 < 2e-16 ***
## LS2004.Nov -0.25272 0.03722 -6.789 1.13e-11 ***
## AO2004.Dec -0.46336 0.04768 -9.718 < 2e-16 ***
## AO2005.Jan 0.21001 0.05129 4.095 4.22e-05 ***
## AO2005.Jun 0.39668 0.05002 7.930 2.19e-15 ***
## AO2006.Jan 0.41973 0.04679 8.969 < 2e-16 ***
## AO2006.Jun 0.52133 0.04725 11.034 < 2e-16 ***
## AO2006.Dec -0.19085 0.04160 -4.588 4.47e-06 ***
## AO2007.Jan 0.35202 0.04432 7.943 1.98e-15 ***
## AO2007.Jun 0.36303 0.04432 8.191 2.59e-16 ***
## AO2010.Jun -0.20396 0.04037 -5.053 4.36e-07 ***
## AO2011.Oct 0.22042 0.03978 5.541 3.01e-08 ***
## AO2011.Dec 0.19854 0.03984 4.983 6.26e-07 ***
## AO2013.Jun -0.40527 0.04064 -9.972 < 2e-16 ***
## AO2014.Jun -0.31716 0.04068 -7.797 6.35e-15 ***
## AO2016.Dec 0.24956 0.04116 6.063 1.34e-09 ***
## MA-Nonseasonal-01 0.68849 0.05725 12.027 < 2e-16 ***
## MA-Seasonal-12 0.63001 0.06814 9.246 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## SEATS adj. ARIMA: (0 1 1)(0 1 1) Obs.: 169 Transform: none
## AICc: -456.5, BIC: -404.1 QS (no seasonality in final):13.25 **
## Box-Ljung (no autocorr.): 26.23 Shapiro (normality): 0.9833 *
capital_trabalho_2b <- final(m)
###############
# Juntando novamente as duas séries
###############
comb <- ts.union(capital_trabalho_2a, capital_trabalho_2b)
capital_trabalho_final <- pmin(comb[,1], comb[,2], na.rm = TRUE)
# Compara a série ajustada com a série original
df <- data.frame(seq(as.Date("1996-01-01"), length = length(capital_trabalho_final), by = "1 month"), capital_trabalho, capital_trabalho_final)
names(df) <- c("Data", "Original", "Filtrada")
p1 <- ggplot(df, aes(Data)) +
geom_line(aes(y = capital_trabalho, colour = "Original"), linetype = "dashed") +
geom_line(aes(y = capital_trabalho_final, colour = "Filtrada")) +
scale_x_date(date_breaks = "12 months", name = "Ano", labels = date_format("%Y"))+
scale_y_continuous(name = "Razão Capital/Trabalho (%)")+
labs(color="Série") +
scale_colour_manual("Variável", breaks = c("Original", "Filtrada"), values = c(cores[1], cores[2]))+
theme_bw() + theme(axis.text.x = element_text(angle=30, hjust = 1, size = 7), legend.position = "top")
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-AntesDepois_CT.pdf", width = 6, height = 3)
p1
#dev.off()
# Essa parte ficou de fora
# Now I'm going to test for unit roots and outliers
teste <- ur.df(capital_trabalho_final, type = "drift", lags = 20, selectlags = "AIC")
summary(teste)
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression drift
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.71942 -0.05589 -0.02009 0.02240 0.84050
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.10407 0.03819 2.725 0.00691 **
## z.lag.1 -0.18025 0.06521 -2.764 0.00615 **
## z.diff.lag1 -0.51120 0.08142 -6.279 1.61e-09 ***
## z.diff.lag2 -0.33937 0.08193 -4.142 4.78e-05 ***
## z.diff.lag3 -0.31427 0.07891 -3.983 9.06e-05 ***
## z.diff.lag4 -0.32914 0.07457 -4.414 1.54e-05 ***
## z.diff.lag5 -0.16080 0.06372 -2.524 0.01227 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.148 on 238 degrees of freedom
## Multiple R-squared: 0.347, Adjusted R-squared: 0.3305
## F-statistic: 21.08 on 6 and 238 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -2.7642 3.8382
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.44 -2.87 -2.57
## phi1 6.47 4.61 3.79
# The value of -2.7642 indicates that we fail to reject the hypothesis of a unit root at 5% sig. level
# Let's take the first difference of this series
capital_trabalho_diff <- diff(capital_trabalho_final)
teste <- ur.df(capital_trabalho_diff, type = "drift", lags = 20, selectlags = "AIC")
# The test statistic of -10,74 makes clear that we reject the null hypothesis of unit root
summary(teste)
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression drift
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.73363 -0.05954 -0.01229 0.03755 0.87206
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.001866 0.009584 0.195 0.84579
## z.lag.1 -3.443603 0.320516 -10.744 < 2e-16 ***
## z.diff.lag1 1.766775 0.284779 6.204 2.43e-09 ***
## z.diff.lag2 1.270467 0.233790 5.434 1.36e-07 ***
## z.diff.lag3 0.822876 0.180244 4.565 8.01e-06 ***
## z.diff.lag4 0.379660 0.124186 3.057 0.00249 **
## z.diff.lag5 0.112135 0.064543 1.737 0.08362 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1497 on 237 degrees of freedom
## Multiple R-squared: 0.7665, Adjusted R-squared: 0.7606
## F-statistic: 129.7 on 6 and 237 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -10.7439 57.7163
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.44 -2.87 -2.57
## phi1 6.47 4.61 3.79
# Compara a série ajustada com a série original e a série diferenciada
df <- data.frame(seq(as.Date("1996-01-01"), length = length(capital_trabalho_final[1:(length(capital_trabalho_final)-1)]), by = "1 month"), capital_trabalho[1:(length(capital_trabalho)-1)], capital_trabalho_final[1:(length(capital_trabalho_final)-1)], capital_trabalho_diff)
names(df) <- c("Data", "Original", "Série Filtrada", "Série diferenciada")
p1 <- ggplot(df, aes(Data)) +
geom_line(aes(y = capital_trabalho[1:(length(capital_trabalho)-1)], colour = "Original")) +
geom_line(aes(y = capital_trabalho_final[1:(length(capital_trabalho_final)-1)], colour = "Filtrada")) +
geom_line(aes(y = capital_trabalho_diff, colour = "Diferenciada")) +
scale_x_date(date_breaks = "12 months", name = "Data", labels = date_format("%m-%Y"))+
scale_y_continuous(name = "Razão Capital/Trabalho")+
labs(color="Variável") +
theme_bw() + theme(axis.text.x = element_text(angle=30, hjust = 1, size = 7))
p1
rm(capital_trabalho_a, capital_trabalho_b, capital_trabalho_2a, capital_trabalho_2b, p1, capital, trabalho, teste)
meses <- ggmonthplot(selic) +
theme_bw() +
scale_y_continuous(name = "Selic (%a.a.)") +
#labs(title = "Média diária e mensal da taxa Selic", x = "Mês", subtitle = "Nenhuma transformação")+
labs(title = "", x = "Mês", subtitle = "")+
theme(axis.title = element_text(size=7), axis.text.x = element_text(angle=25, hjust = 1, size = 7))
# Gráfico por ano e mês
season <- ggseasonplot(selic, year.labels = TRUE) +
geom_point() +
theme_bw() +
scale_y_continuous(name = "Selic (%a.a.)") +
#labs(title = "Média mensal da taxa Selic", x = "Mês", subtitle = "Nenhuma transformação")+
labs(title = "", x = "Mês", subtitle = "")+
theme(axis.title = element_text(size=7), axis.text.x = element_text(angle=25, hjust = 1, size = 7))
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Season_SELIC.pdf", width = 6, height = 3)
season
#dev.off()
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Month_SELIC.pdf", width = 6, height = 3)
meses
#dev.off()
bp_ts <- breakpoints(selic ~ 1)
ci_ts <- confint(bp_ts)
Data <- seq(as.Date("1996-01-01"), length = length(selic), by = "1 month")
df1 <- melt(data.frame(Data,selic), id.vars = "Data")
names(df1) <- c("Data", "Variavel", "Valor")
p1 <- ggplot(df1[which(df1$Variavel == "selic"),], aes(Data, Valor, colour = Variavel)) +
geom_line(alpha = 1, show.legend=F, colour = cores[1])+
scale_y_continuous(name="Selic (%a.a.)") +
scale_x_date(date_breaks = "12 months", name = "Data", labels = date_format("%m-%Y"))+
geom_vline(xintercept = Data[bp_ts$breakpoints], linetype="longdash")+
geom_segment(aes(x = Data[ci_ts$confint[1]], y = min(selic), xend = Data[ci_ts$confint[5]], yend = min(selic)))+
geom_segment(aes(x = Data[ci_ts$confint[2]], y = min(selic), xend = Data[ci_ts$confint[6]], yend = min(selic)))+
theme_bw()
p1 <- p1 + theme(axis.text.x = element_text(angle=25, hjust = 1, size = 6), legend.position = "none")
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Quebra_SELIC.pdf", width = 6, height = 3)
p1
#dev.off()
###########
# Dividindo a selic em três pedaços
##########
# Salvando três séries para passar o seasonal
selic_a <- selic[1:(bp_ts$breakpoints[1]-1)]
selic_b <- selic[(bp_ts$breakpoints[1]):(bp_ts$breakpoints[2]-1)]
selic_c <- selic[(bp_ts$breakpoints[2]):(length(selic))]
selic_a <- ts(selic_a, start = c(1996, 01, 01), frequency = 12)
selic_b <- ts(selic_b, start = c(1999, 05, 01), frequency = 12)
selic_c <- ts(selic_c, start = c(2006, 08, 01), frequency = 12)
selic_2a <- selic_a
m <- seas(x = selic_b, transform.function = "none", regression.aictest = NULL)
qs(m)
## qs p-val
## qsori 30.28836 0.00000
## qsorievadj 30.28836 0.00000
## qsrsd 0.00000 1.00000
## qssadj 3.00726 0.22232
## qssadjevadj 3.00726 0.22232
## qsirr 0.00000 1.00000
## qsirrevadj 0.00000 1.00000
summary(m)
##
## Call:
## seas(x = selic_b, transform.function = "none", regression.aictest = NULL)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## AR-Nonseasonal-01 -0.19030 0.14589 -1.304 0.192
## AR-Nonseasonal-02 0.09671 0.09194 1.052 0.293
## AR-Nonseasonal-03 0.51926 0.08351 6.218 5.03e-10 ***
## MA-Nonseasonal-01 0.12082 0.17475 0.691 0.489
## MA-Seasonal-12 0.99913 0.12930 7.727 1.10e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## SEATS adj. ARIMA: (3 1 1)(0 1 1) Obs.: 87 Transform: none
## AICc: 306.6, BIC: 319.2 QS (no seasonality in final):3.007
## Box-Ljung (no autocorr.): 44.68 ** Shapiro (normality): 0.9865
## Messages generated by X-13:
## Warnings:
## - At least one visually significant trading day peak has
## been found in one or more of the estimated spectra.
selic_2b <- final(m)
m <- seas(x = selic_c, transform.function = "none", regression.aictest = NULL)
qs(m)
## qs p-val
## qsori 45.47230 0.00000
## qsorievadj 45.47230 0.00000
## qsrsd 0.00000 1.00000
## qssadj 2.90012 0.23456
## qssadjevadj 2.90012 0.23456
## qsirr 0.00000 1.00000
## qsirrevadj 0.00000 1.00000
## qssori 31.25379 0.00000
## qssorievadj 31.25379 0.00000
## qssrsd 0.00000 1.00000
## qsssadj 2.79444 0.24728
## qsssadjevadj 2.79444 0.24728
## qssirr 0.00000 1.00000
## qssirrevadj 0.00000 1.00000
summary(m)
##
## Call:
## seas(x = selic_c, transform.function = "none", regression.aictest = NULL)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## AR-Nonseasonal-01 -0.17009 0.10795 -1.576 0.11511
## AR-Nonseasonal-02 0.21991 0.07042 3.123 0.00179 **
## AR-Nonseasonal-03 0.58243 0.06440 9.044 < 2e-16 ***
## MA-Nonseasonal-01 0.29636 0.13073 2.267 0.02339 *
## MA-Seasonal-12 0.99998 0.09303 10.749 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## SEATS adj. ARIMA: (3 1 1)(0 1 1) Obs.: 139 Transform: none
## AICc: 311.3, BIC: 327.6 QS (no seasonality in final): 2.9
## Box-Ljung (no autocorr.): 61.92 *** Shapiro (normality): 0.9843
## Messages generated by X-13:
## Warnings:
## - At least one visually significant trading day peak has
## been found in one or more of the estimated spectra.
selic_2c <- final(m)
###############
# Juntando novamente as três séries
###############
comb <- ts.union(selic_2a, selic_2b, selic_2c)
selic_final <- pmin(comb[,1], comb[,2], comb[,3], na.rm = TRUE)
# Compara a série ajustada com a série original
df <- data.frame(seq(as.Date("1996-01-01"), length = length(selic_final), by = "1 month"), selic, selic_final)
names(df) <- c("Data", "Original", "Série Filtrada")
p1 <- ggplot(df, aes(Data)) +
geom_line(aes(y = selic, colour = "Original"), linetype = "dashed") +
geom_line(aes(y = selic_final, colour = "Filtrada")) +
scale_x_date(date_breaks = "12 months", name = "Ano", labels = date_format("%Y"))+
scale_y_continuous(name = "Selic (%a.a.)")+
labs(color="Série") +
scale_colour_manual("Variável", breaks = c("Original", "Filtrada"), values = c(cores[1], cores[2]))+
theme_bw() + theme(axis.text.x = element_text(angle=30, hjust = 1, size = 7), legend.position = "top")
p1
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-AntesDepois_SELIC.pdf", width = 6, height = 3)
p1
#dev.off()
teste <- ur.df(selic_final, type = "drift", selectlags = "AIC", lags = 20)
summary(teste)
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression drift
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.4155 -0.8920 -0.1325 0.7859 21.8141
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.55727 0.45884 1.215 0.2258
## z.lag.1 -0.04258 0.02739 -1.555 0.1213
## z.diff.lag1 -0.07486 0.06754 -1.108 0.2688
## z.diff.lag2 -0.12590 0.06436 -1.956 0.0516 .
## z.diff.lag3 -0.09387 0.06487 -1.447 0.1492
## z.diff.lag4 -0.09785 0.06484 -1.509 0.1326
## z.diff.lag5 -0.05325 0.06442 -0.827 0.4092
## z.diff.lag6 0.05328 0.06387 0.834 0.4051
## z.diff.lag7 -0.27783 0.06296 -4.413 1.55e-05 ***
## z.diff.lag8 -0.09719 0.06503 -1.495 0.1364
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.594 on 235 degrees of freedom
## Multiple R-squared: 0.1435, Adjusted R-squared: 0.1107
## F-statistic: 4.376 on 9 and 235 DF, p-value: 2.692e-05
##
##
## Value of test-statistic is: -1.5549 1.4189
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.44 -2.87 -2.57
## phi1 6.47 4.61 3.79
# Eu não acho que faz muito sentido diferenciar a selic pra tirar a raiz unitária... mas é uma possibilidade pra ver se são as variações na selic que impactam nas variações da razão capital trabalho
rm(p1, p2, selic_4390, selic_2a, selic_2b, selic_2c, selic_a, selic_b, selic_c, teste)
meses <- ggmonthplot(swap90) +
theme_bw() +
scale_y_continuous(name = "Swap DI 90d (%a.a)") +
#labs(title = "Média diária e mensal da taxa Selic", x = "Mês", subtitle = "Nenhuma transformação")+
labs(title = "", x = "Mês", subtitle = "")+
theme(axis.title = element_text(size=7), axis.text.x = element_text(angle=25, hjust = 1, size = 7))
# Gráfico por ano e mês
season <- ggseasonplot(swap90, year.labels = TRUE) +
geom_point() +
theme_bw() +
scale_y_continuous(name = "Swap DI 90d (%a.a.)") +
#labs(title = "Média mensal da taxa swapDI 90d", x = "Mês", subtitle = "Nenhuma transformação")+
labs(title = "", x = "Mês", subtitle = "")+
theme(axis.title = element_text(size=7), axis.text.x = element_text(angle=25, hjust = 1, size = 7))
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Season_SWAP.pdf", width = 6, height = 3)
season
#dev.off()
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Month_SWAP.pdf", width = 6, height = 3)
meses
#dev.off()
bp_ts <- breakpoints(swap90 ~ 1)
ci_ts <- confint(bp_ts)
#m <- seas(swap90, transform.function = "none", regression.aictest = NULL)
#summary(m) # Series should not be a candidate for seasonal adjustment because the spectrum of the prior adjusted series (Table B1) has no visually significant seasonal peaks.
Data <- seq(as.Date("1999-09-01"), length = length(swap90), by = "1 month")
df1 <- melt(data.frame(Data,swap90), id.vars = "Data")
names(df1) <- c("Data", "Variavel", "Valor")
p1 <- ggplot(df1[which(df1$Variavel == "swap90"),], aes(Data, Valor, colour = Variavel)) +
geom_line(alpha = 1, show.legend=F, colour = cores[1])+
scale_y_continuous(name="Swap DI 90d (%a.a.)") +
scale_x_date(date_breaks = "12 months", name = "Data", labels = date_format("%m-%Y"))+
geom_vline(xintercept = Data[bp_ts$breakpoints], linetype="longdash")+
geom_segment(aes(x = Data[ci_ts$confint[1]], y = min(swap90), xend = Data[ci_ts$confint[5]], yend = min(swap90)))+
geom_segment(aes(x = Data[ci_ts$confint[2]], y = min(swap90), xend = Data[ci_ts$confint[6]], yend = min(swap90)))+
theme_bw()
p1 <- p1 + theme(axis.text.x = element_text(angle=25, hjust = 1, size = 6), legend.position = "none")
p1
## Cortar a selic a partir de 1999-09-01
selic_cortada <- window(selic_final, c(1999, 09))
df8 <- data.frame(Data, swap90, selic_cortada)
names(df8) <- c("Data", "Swap", "Selic")
df9 <- melt(data = df8, id.vars = "Data")
p9 <- ggplot(df9, aes(Data, value, colour = variable))+
geom_line(alpha = 1, aes(linetype = variable))+
labs(title="", y = "Taxa (%a.a.)", x = "Ano", color = "Taxa") +
scale_colour_brewer(palette = "Set1")+
scale_x_date(date_breaks = "1 year", name = "Ano", labels = date_format("%Y"))+
theme_bw()
p9 <- p9 + labs(linetype = "Taxa")
p9 <- p9 + labs(colour = "Taxa")
p9 <- p9 + theme(legend.position = "top", legend.key.size = unit(.5, "cm"), axis.text.x = element_text(angle = 25, hjust = 1, size = 7), axis.title.y = element_text(size = 7), axis.title.x = element_text(size = 7))
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Swap_Selic.pdf", width = 6, height = 3)
p9
#dev.off()
#######################
# PIB Mensal #
#######################
cores <- brewer.pal(6, "Dark2")
meses <- ggmonthplot(PIBmensal) +
theme_bw() +
scale_y_continuous(name = "PIB mensal (R$ - milhões)") +
labs(title = "", x = "Mês", subtitle = "")+
theme(axis.title = element_text(size=7), axis.text.x = element_text(angle=25, hjust = 1, size = 7))
#labs(title = "Média diária e mensal da variação do PIB", x = "Mês", subtitle = "Nenhuma transformação")
# Gráfico por ano e mês
season <- ggseasonplot(PIBmensal, year.labels = TRUE) +
geom_point() +
theme_bw() +
scale_y_continuous(name = "PIB mensal (R$ - milhões)") +
labs(title = "", x = "Mês", subtitle = "")+
theme(axis.title = element_text(size=7), axis.text.x = element_text(angle=25, hjust = 1, size = 7))
#labs(title = "Média mensal da da variação do PIB", x = "Mês", subtitle = "Nenhuma transformação")
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Season_PIB.pdf", width = 6, height = 3)
season
#dev.off()
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Month_PIB.pdf", width = 6, height = 3)
meses
#dev.off()
bp_ts <- breakpoints(PIBmensal ~ 1)
ci_ts <- confint(bp_ts)
Data <- seq(as.Date("1996-01-01"), length = length(PIBmensal), by = "1 month")
df1 <- melt(data.frame(Data,PIBmensal), id.vars = "Data")
names(df1) <- c("Data", "Variavel", "Valor")
p1 <- ggplot(df1[which(df1$Variavel == "PIBmensal"),], aes(Data, Valor, colour = Variavel)) +
geom_line(alpha = 1, show.legend=F, colour = cores[1])+
scale_y_continuous(name="PIB mensal (R$ milhões)") +
scale_x_date(date_breaks = "12 months", name = "Data", labels = date_format("%m-%Y"))+
geom_vline(xintercept = Data[bp_ts$breakpoints], linetype="longdash")+
geom_segment(aes(x = Data[ci_ts$confint[1]], y = min(PIBmensal), xend = Data[ci_ts$confint[5]], yend = min(PIBmensal)))+
geom_segment(aes(x = Data[ci_ts$confint[2]], y = min(PIBmensal), xend = Data[ci_ts$confint[6]], yend = min(PIBmensal)))+
geom_segment(aes(x = Data[ci_ts$confint[3]], y = min(PIBmensal), xend = Data[ci_ts$confint[7]], yend = min(PIBmensal)))+
geom_segment(aes(x = Data[ci_ts$confint[4]], y = min(PIBmensal), xend = Data[ci_ts$confint[8]], yend = min(PIBmensal)))+
theme_bw()
p1 <- p1 + theme(axis.text.x = element_text(angle=25, hjust = 1, size = 6), legend.position = "none")
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Quebra_PIB.pdf", width = 6, height = 3)
p1
#dev.off()
m <- seas(x = PIBmensal, transform.function = "none", regression.aictest = NULL)
qs(m)
## qs p-val
## qsori 223.05943 0.00000
## qsorievadj 223.05943 0.00000
## qsrsd 2.04455 0.35978
## qssadj 0.11717 0.94310
## qssadjevadj 0.11717 0.94310
## qsirr 0.00000 1.00000
## qsirrevadj 0.00000 1.00000
## qssori 73.70678 0.00000
## qssorievadj 73.70678 0.00000
## qssrsd 0.65785 0.71970
## qsssadj 0.01014 0.99494
## qsssadjevadj 0.01014 0.99494
## qssirr 0.00000 1.00000
## qssirrevadj 0.00000 1.00000
summary(m)
##
## Call:
## seas(x = PIBmensal, transform.function = "none", regression.aictest = NULL)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## AR-Nonseasonal-01 -0.83700 0.13651 -6.131 8.71e-10 ***
## AR-Nonseasonal-02 -0.37993 0.05744 -6.615 3.72e-11 ***
## MA-Nonseasonal-01 -0.57124 0.14263 -4.005 6.20e-05 ***
## MA-Seasonal-12 0.72433 0.04796 15.104 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## SEATS adj. ARIMA: (2 1 1)(0 1 1) Obs.: 267 Transform: none
## AICc: 5370, BIC: 5388 QS (no seasonality in final):0.1172
## Box-Ljung (no autocorr.): 59.13 *** Shapiro (normality): 0.997
## Messages generated by X-13:
## Warnings:
## - At least one visually significant trading day peak has
## been found in one or more of the estimated spectra.
# Even though the series presents structural breaks, I'm not dividing to make the adjustment because for the individual pieces the seasonal adjustment is not effective
# Salva a série final em uma nova variável
PIB2 <- final(m)
# Compara a série ajustada com a série original
df <- data.frame(seq(as.Date("1996-01-01"), length = length(PIBmensal), by = "1 month"), PIBmensal, PIB2)
names(df) <- c("Data", "Original", "Série Filtrada")
p2 <- ggplot(df, aes(Data)) +
geom_line(aes(y = PIBmensal, colour = "Original"), linetype = "dashed") +
geom_line(aes(y = PIB2, colour = "Filtrada")) +
scale_x_date(date_breaks = "12 months", name = "Ano", labels = date_format("%Y"))+
scale_y_continuous(name = "PIB Mensal (R$ milhões)")+
labs(color="Série") +
scale_colour_manual("Variável", breaks = c("Original", "Filtrada"), values = c(cores[1], cores[2]))+
theme_bw() + theme(axis.text.x = element_text(angle=30, hjust = 1, size = 7), legend.position = "top")
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-AntesDepois_PIB.pdf", width = 6, height = 3)
p2
#dev.off()
# Now we transform to GDP growth rate
PIBm.df <- ur.df(PIB2, type = "trend", selectlags = "AIC", lags = 20)
summary(PIBm.df)
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -25069.8 -4087.3 88.1 4655.8 15070.3
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.906e+03 3.433e+03 2.011 0.04548 *
## z.lag.1 -2.806e-02 1.661e-02 -1.690 0.09250 .
## tt 4.090e+01 2.675e+01 1.529 0.12774
## z.diff.lag1 -2.028e-01 6.625e-02 -3.061 0.00247 **
## z.diff.lag2 -1.240e-01 6.741e-02 -1.840 0.06713 .
## z.diff.lag3 4.834e-02 6.779e-02 0.713 0.47652
## z.diff.lag4 -1.466e-01 6.769e-02 -2.166 0.03140 *
## z.diff.lag5 1.144e-01 6.827e-02 1.675 0.09523 .
## z.diff.lag6 1.755e-01 6.793e-02 2.584 0.01040 *
## z.diff.lag7 3.474e-02 6.808e-02 0.510 0.61033
## z.diff.lag8 4.757e-02 6.785e-02 0.701 0.48400
## z.diff.lag9 1.069e-01 6.764e-02 1.580 0.11554
## z.diff.lag10 8.834e-03 6.804e-02 0.130 0.89681
## z.diff.lag11 8.502e-02 6.788e-02 1.253 0.21164
## z.diff.lag12 -2.062e-02 6.812e-02 -0.303 0.76244
## z.diff.lag13 9.059e-02 6.810e-02 1.330 0.18483
## z.diff.lag14 2.891e-02 6.799e-02 0.425 0.67113
## z.diff.lag15 1.005e-01 6.871e-02 1.463 0.14482
## z.diff.lag16 -5.558e-02 6.828e-02 -0.814 0.41655
## z.diff.lag17 1.853e-01 6.837e-02 2.710 0.00724 **
## z.diff.lag18 1.134e-01 6.839e-02 1.659 0.09855 .
## z.diff.lag19 -1.103e-01 6.716e-02 -1.642 0.10192
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6869 on 224 degrees of freedom
## Multiple R-squared: 0.299, Adjusted R-squared: 0.2333
## F-statistic: 4.55 on 21 and 224 DF, p-value: 2.706e-09
##
##
## Value of test-statistic is: -1.6896 1.9696 1.5483
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -3.98 -3.42 -3.13
## phi2 6.15 4.71 4.05
## phi3 8.34 6.30 5.36
# Since it is non-stationary, we take log difference
PIB <- diff(log(PIB2), 1)
autoplot(PIB)
PIB.df <- ur.df(PIB, type = "none", selectlags = "AIC", lags = 20)
summary(PIB.df)
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.057193 -0.007917 0.002290 0.010353 0.046704
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.42364 0.24624 -1.720 0.086730 .
## z.diff.lag1 -0.75572 0.24622 -3.069 0.002410 **
## z.diff.lag2 -0.87318 0.24710 -3.534 0.000498 ***
## z.diff.lag3 -0.92117 0.24993 -3.686 0.000286 ***
## z.diff.lag4 -1.13965 0.25271 -4.510 1.05e-05 ***
## z.diff.lag5 -1.02745 0.25598 -4.014 8.15e-05 ***
## z.diff.lag6 -0.90695 0.25810 -3.514 0.000534 ***
## z.diff.lag7 -0.90280 0.25660 -3.518 0.000526 ***
## z.diff.lag8 -0.83808 0.25418 -3.297 0.001136 **
## z.diff.lag9 -0.70885 0.24920 -2.845 0.004859 **
## z.diff.lag10 -0.72064 0.24341 -2.961 0.003400 **
## z.diff.lag11 -0.65663 0.23631 -2.779 0.005922 **
## z.diff.lag12 -0.69323 0.22812 -3.039 0.002657 **
## z.diff.lag13 -0.64869 0.21712 -2.988 0.003124 **
## z.diff.lag14 -0.63229 0.20346 -3.108 0.002130 **
## z.diff.lag15 -0.54885 0.18955 -2.896 0.004160 **
## z.diff.lag16 -0.63232 0.17031 -3.713 0.000259 ***
## z.diff.lag17 -0.41204 0.14433 -2.855 0.004711 **
## z.diff.lag18 -0.31236 0.11932 -2.618 0.009452 **
## z.diff.lag19 -0.34610 0.09137 -3.788 0.000195 ***
## z.diff.lag20 -0.23364 0.06153 -3.797 0.000188 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01582 on 224 degrees of freedom
## Multiple R-squared: 0.7146, Adjusted R-squared: 0.6878
## F-statistic: 26.7 on 21 and 224 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -1.7205
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62
# Let's try to plot everything together
df <- data.frame(seq(as.Date("1996-01-01"), length = length(PIBmensal[-length(PIBmensal)]), by = "1 month"), PIBmensal[-length(PIBmensal)]/10^(6), PIB2[-length(PIB2)]/10^(6), PIB)
names(df) <- c("Data", "Original", "Série Filtrada", "Série diferenciada")
p3 <- ggplot(df, aes(Data)) +
geom_line(aes(y = PIBmensal[-length(PIBmensal)]/10^(6), colour = "Original")) +
geom_line(aes(y = PIB2[-length(PIB2)]/10^(6), colour = "Filtrada")) +
geom_line(aes(y = PIB, colour = "Diferenciada")) +
scale_x_date(date_breaks = "12 months", name = "Data", labels = date_format("%Y"))+
scale_y_continuous(name = "PIB Mensal (base = 03/18)")+
labs(color="Variável") +
theme_bw()
p3 + theme(axis.text.x = element_text(angle=25, hjust = 1, size = 8))
#######################
# Câmbio #
#######################
cores <- brewer.pal(6, "Dark2")
meses <- ggmonthplot(cambio_raw) +
theme_bw() +
scale_y_continuous(name = "Taxa de Câmbio Efetiva Real (índice)") +
labs(title = "", x = "Mês", subtitle = "")+
theme(axis.title = element_text(size=7), axis.text.x = element_text(angle=25, hjust = 1, size = 7))
#labs(title = "Média diária e mensal da taxa de câmbio", x = "Month", subtitle = "No data transformation")
# Gráfico por ano e mês
season <- ggseasonplot(cambio_raw, year.labels = TRUE) +
geom_point() +
theme_bw() +
scale_y_continuous(name = "Taxa de Câmbio Efetiva Real (índice)") +
labs(title = "", x = "Mês", subtitle = "")+
theme(axis.title = element_text(size=7), axis.text.x = element_text(angle=25, hjust = 1, size = 7))
#labs(title = "Monthly average of exchange rate", x = "Month", subtitle = "No data transformation")
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Season_CAMBIO.pdf", width = 6, height = 3)
season
#dev.off()
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Month_CAMBIO.pdf", width = 6, height = 3)
meses
#dev.off()
bp_ts <- breakpoints(cambio_raw ~ 1)
ci_ts <- confint(bp_ts)
Data <- seq(as.Date("1996-01-01"), length = length(cambio_raw), by = "1 month")
df1 <- melt(data.frame(Data,cambio_raw), id.vars = "Data")
names(df1) <- c("Data", "Variavel", "Valor")
p1 <- ggplot(df1[which(df1$Variavel == "cambio_raw"),], aes(Data, Valor, colour = Variavel)) +
geom_line(alpha = 1, show.legend=F, colour = cores[1])+
scale_y_continuous(name="Taxa de Câmbio Efetiva Real (índice)") +
scale_x_date(date_breaks = "12 months", name = "Date", labels = date_format("%m-%Y"))+
geom_vline(xintercept = Data[bp_ts$breakpoints], linetype="longdash")+
geom_segment(aes(x = Data[ci_ts$confint[1]], y = min(cambio_raw), xend = Data[ci_ts$confint[5]], yend = min(cambio_raw)))+
geom_segment(aes(x = Data[ci_ts$confint[2]], y = min(cambio_raw), xend = Data[ci_ts$confint[7]], yend = min(cambio_raw)))+
geom_segment(aes(x = Data[ci_ts$confint[3]], y = min(cambio_raw), xend = Data[ci_ts$confint[8]], yend = min(cambio_raw)))+
geom_segment(aes(x = Data[ci_ts$confint[4]], y = min(cambio_raw), xend = Data[ci_ts$confint[9]], yend = min(cambio_raw)))+
geom_segment(aes(x = Data[ci_ts$confint[5]], y = min(cambio_raw), xend = Data[ci_ts$confint[10]], yend = min(cambio_raw)))+
theme_bw()
p1 <- p1 + theme(axis.text.x = element_text(angle=25, hjust = 1, size = 6), legend.position = "none")
p1
m <- seas(x = cambio_raw, transform.function = "none", regression.aictest = NULL)
qs(m)
## qs p-val
## qsori 0.00000 1.00000
## qsorievadj 0.00000 1.00000
## qsrsd 0.00000 1.00000
## qssadj 0.00000 1.00000
## qssadjevadj 0.00000 1.00000
## qsirr 0.57866 0.74876
## qsirrevadj 0.00000 1.00000
## qssori 0.00000 1.00000
## qssorievadj 0.00000 1.00000
## qssrsd 0.00000 1.00000
## qsssadj 0.00000 1.00000
## qsssadjevadj 0.00000 1.00000
## qssirr 0.00091 0.99954
## qssirrevadj 0.00091 0.99954
summary(m)
##
## Call:
## seas(x = cambio_raw, transform.function = "none", regression.aictest = NULL)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## AO1999.Jan 17.02417 3.10157 5.489 4.04e-08 ***
## LS1999.Feb 38.41276 5.45786 7.038 1.95e-12 ***
## AO2002.Oct 13.48199 1.51561 8.895 < 2e-16 ***
## AO2003.Jan -10.34927 1.51561 -6.828 8.58e-12 ***
## AO2008.Dec 7.21518 1.47400 4.895 9.83e-07 ***
## MA-Nonseasonal-01 -0.54829 0.05163 -10.619 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## SEATS adj. ARIMA: (0 1 1) Obs.: 266 Transform: none
## AICc: 1367, BIC: 1391 QS (no seasonality in final): 0
## Box-Ljung (no autocorr.): 30.11 Shapiro (normality): 0.9482 ***
## Messages generated by X-13:
## Warnings:
## - At least one visually significant seasonal peak has been
## found in one or more of the estimated spectra.
##
## Notes:
## - Unable to test LS1999.Jan due to regression matrix
## singularity.
## - Unable to test LS1999.Jan due to regression matrix
## singularity.
## - Unable to test LS2015.Aug due to regression matrix
## singularity.
## - Unable to test LS2008.Sep due to regression matrix
## singularity.
cambio <- cambio_raw
# Não tem evidência que precisa ajuste sazonal na série toda
# Como não fiz nenhuma transformação não tem muito o que plotar de gráfico aqui
#######################
# IPCA #
#######################
cores <- brewer.pal(6, "Dark2")
meses <- ggmonthplot(ipca) +
theme_bw() +
scale_y_continuous(name = "Taxa de Inflação (IPCA - % a.a.)") +
labs(title = "", x = "Mês", subtitle = "")+
theme(axis.title = element_text(size=7), axis.text.x = element_text(angle=25, hjust = 1, size = 7))
#labs(title = "Monthly average of the inflation index", x = "Month", subtitle = "No data transformation")
# Gráfico por ano e mês
season <- ggseasonplot(ipca, year.labels = TRUE) +
geom_point() +
theme_bw() +
scale_y_continuous(name = "Taxa de Inflação (IPCA - % a.a.)") +
labs(title = "", x = "Mês", subtitle = "")+
theme(axis.title = element_text(size=7), axis.text.x = element_text(angle=25, hjust = 1, size = 7))
#labs(title = "Monthly average of the inflation index", x = "Month", subtitle = "No data transformation")
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Season_IPCA.pdf", width = 6, height = 3)
season
#dev.off()
#pdf(file = "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Imagens\\Fig-Month_IPCA.pdf", width = 6, height = 3)
meses
#dev.off()
bp_ts <- breakpoints(ipca ~ 1)
ci_ts <- confint(bp_ts)
Data <- seq(as.Date("1996-01-01"), length = length(ipca), by = "1 month")
df1 <- melt(data.frame(Data,ipca), id.vars = "Data")
names(df1) <- c("Data", "Variavel", "Valor")
p1 <- ggplot(df1[which(df1$Variavel == "ipca"),], aes(Data, Valor, colour = Variavel)) +
geom_line(alpha = 1, show.legend=F, colour = cores[1])+
scale_y_continuous(name="Inflation (% monthly)") +
scale_x_date(date_breaks = "12 months", name = "Date", labels = date_format("%m-%Y"))+
geom_vline(xintercept = Data[bp_ts$breakpoints], linetype="longdash")+
geom_segment(aes(x = Data[ci_ts$confint[1]], y = min(ipca), xend = Data[ci_ts$confint[5]], yend = min(ipca)))+
geom_segment(aes(x = Data[ci_ts$confint[2]], y = min(ipca), xend = Data[ci_ts$confint[6]], yend = min(ipca)))+
theme_bw()
p1 <- p1 + theme(axis.text.x = element_text(angle=25, hjust = 1, size = 6), legend.position = "none")
p1
# Now I divide the series in 3 different pieces to apply the seasonal filter
# Salvando três séries para passar o seasonal
ipca_a <- ipca[1:(bp_ts$breakpoints[1]-1)]
ipca_b <- ipca[(bp_ts$breakpoints[1]):(bp_ts$breakpoints[2]-1)]
ipca_c <- ipca[(bp_ts$breakpoints[2]):(length(ipca))]
ipca_a <- ts(ipca_a, start = c(1996, 01, 01), frequency = 12)
ipca_b <- ts(ipca_b, start = c(2002, 03, 01), frequency = 12)
ipca_c <- ts(ipca_c, start = c(2005, 06, 01), frequency = 12)
# There is no evidence of seasonal component in either the complete series nor the pieces
m <- seas(x = ipca_a, transform.function = "none", regression.aictest = NULL)
qs(m)
## qs p-val
## qsori 0.00000 1.00000
## qsorievadj 0.00000 1.00000
## qsrsd 0.52144 0.77050
## qssadj 0.00000 1.00000
## qssadjevadj 0.00000 1.00000
## qsirr 0.00000 1.00000
## qsirrevadj 0.00000 1.00000
## qssrsd 0.35015 0.83939
summary(m)
##
## Call:
## seas(x = ipca_a, transform.function = "none", regression.aictest = NULL)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## AR-Nonseasonal-01 0.79459 0.06821 11.649 <2e-16 ***
## MA-Seasonal-12 0.50638 0.09393 5.391 7e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## SEATS adj. ARIMA: (1 1 0)(0 0 1) Obs.: 74 Transform: none
## AICc: 92.27, BIC: 98.79 QS (no seasonality in final): 0
## Box-Ljung (no autocorr.): 22.07 Shapiro (normality): 0.984
## Messages generated by X-13:
## Warnings:
## - Series should not be a candidate for seasonal adjustment
## because the spectrum of the original series (Table A1 or
## B1) has no visually significant seasonal peaks.
##
## Notes:
## - Model used for SEATS decomposition is different from the
## model estimated in the regARIMA modeling module of
## X-13ARIMA-SEATS.
# Não tem evidência que precisa ajuste sazonal na primeira parte
m <- seas(x = ipca_b, transform.function = "none", regression.aictest = NULL)
qs(m)
## qs p-val
## qsori 0 1
## qsorievadj 0 1
## qsrsd 0 1
## qssadj 0 1
## qssadjevadj 0 1
## qsirr 0 1
## qsirrevadj 0 1
summary(m)
##
## Call:
## seas(x = ipca_b, transform.function = "none", regression.aictest = NULL)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## LS2002.Nov 1.4617 0.3866 3.781 0.000156 ***
## LS2003.Nov -1.5678 0.3866 -4.056 5e-05 ***
## AR-Nonseasonal-01 0.7847 0.0954 8.226 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## SEATS adj. ARIMA: (1 1 0) Obs.: 39 Transform: none
## AICc: 64.01, BIC: 69.35 QS (no seasonality in final): 0
## Box-Ljung (no autocorr.): 33.2 . Shapiro (normality): 0.9852
## Messages generated by X-13:
## Warnings:
## - Series should not be a candidate for seasonal adjustment
## because the spectrum of the prior adjusted series (Table
## B1) has no visually significant seasonal peaks.
##
## Notes:
## - The program cannot perform hypothesis tests for kurtosis
## on less than 50 observations.
# Não tem evidência que precisa ajuste sazonal na segunda parte
m <- seas(x = ipca_c, transform.function = "none", regression.aictest = NULL)
qs(m)
## qs p-val
## qsori 0.00000 1.00000
## qsorievadj 0.00000 1.00000
## qsrsd 2.06009 0.35699
## qssadj 0.00000 1.00000
## qssadjevadj 0.00000 1.00000
## qsirr 0.00000 1.00000
## qsirrevadj 0.00000 1.00000
## qssori 0.00000 1.00000
## qssorievadj 0.00000 1.00000
## qssrsd 1.09881 0.57729
## qsssadj 0.00000 1.00000
## qsssadjevadj 0.00000 1.00000
## qssirr 0.00000 1.00000
## qssirrevadj 0.00000 1.00000
summary(m)
##
## Call:
## seas(x = ipca_c, transform.function = "none", regression.aictest = NULL)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## AR-Nonseasonal-01 0.63263 0.05707 11.09 <2e-16 ***
## MA-Seasonal-12 0.99989 0.06319 15.82 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## SEATS adj. ARIMA: (1 1 0)(0 0 1) Obs.: 153 Transform: none
## AICc: -19.97, BIC: -11.06 QS (no seasonality in final): 0
## Box-Ljung (no autocorr.): 34.49 . Shapiro (normality): 0.993
## Messages generated by X-13:
## Warnings:
## - Series should not be a candidate for seasonal adjustment
## because the spectrum of the original series (Table A1 or
## B1) has no visually significant seasonal peaks.
##
## Notes:
## - Model used for SEATS decomposition is different from the
## model estimated in the regARIMA modeling module of
## X-13ARIMA-SEATS.
# Não tem evidência que precisa ajuste sazonal na terceira parte
m <- seas(x = ipca, transform.function = "none", regression.aictest = NULL)
qs(m)
## qs p-val
## qsori 0.00000 1.00000
## qsorievadj 0.00000 1.00000
## qsrsd 1.84107 0.39830
## qssadj 0.00000 1.00000
## qssadjevadj 0.00000 1.00000
## qsirr 0.00000 1.00000
## qsirrevadj 0.00000 1.00000
## qssori 0.00000 1.00000
## qssorievadj 0.00000 1.00000
## qssrsd 2.06590 0.35595
## qsssadj 0.00000 1.00000
## qsssadjevadj 0.00000 1.00000
## qssirr 0.00000 1.00000
## qssirrevadj 0.00000 1.00000
summary(m)
##
## Call:
## seas(x = ipca, transform.function = "none", regression.aictest = NULL)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## LS2003.Jul -0.55724 0.12823 -4.346 1.39e-05 ***
## AR-Nonseasonal-01 0.76739 0.03792 20.239 < 2e-16 ***
## MA-Seasonal-12 0.89032 0.02928 30.404 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## SEATS adj. ARIMA: (1 1 0)(0 0 1) Obs.: 266 Transform: none
## AICc: 179, BIC: 193.2 QS (no seasonality in final): 0
## Box-Ljung (no autocorr.): 14 Shapiro (normality): 0.9356 ***
## Messages generated by X-13:
## Warnings:
## - Series should not be a candidate for seasonal adjustment
## because the spectrum of the prior adjusted series (Table
## B1) has no visually significant seasonal peaks.
##
## Notes:
## - Model used for SEATS decomposition is different from the
## model estimated in the regARIMA modeling module of
## X-13ARIMA-SEATS.
# Não tem evidência que precisa ajuste sazonal na série toda
# Como não fiz nenhuma transformação não tem muito o que plotar de gráfico aqui
##
## <table style="text-align:center"><tr><td colspan="6" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"></td><td>Capital_trabalho</td><td>Swap</td><td>PIB</td><td>Cambio</td><td>IPCA</td></tr>
## <tr><td colspan="6" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">Observações</td><td>266</td><td>266</td><td>266</td><td>266</td><td>266</td></tr>
## <tr><td style="text-align:left">Mínimo</td><td>-8.139</td><td>6.540</td><td>-6.531</td><td>66.560</td><td>1.646</td></tr>
## <tr><td style="text-align:left">1o quartil</td><td>44.822</td><td>10.713</td><td>-0.909</td><td>81.070</td><td>4.809</td></tr>
## <tr><td style="text-align:left">Média</td><td>55.770</td><td>13.991</td><td>0.294</td><td>97.465</td><td>6.828</td></tr>
## <tr><td style="text-align:left">Mediana</td><td>51.240</td><td>13.160</td><td>0.372</td><td>95.610</td><td>6.271</td></tr>
## <tr><td style="text-align:left">3o quartil</td><td>63.688</td><td>17.390</td><td>1.625</td><td>108.060</td><td>7.670</td></tr>
## <tr><td style="text-align:left">Máximo</td><td>151.001</td><td>27.490</td><td>5.314</td><td>171.030</td><td>21.988</td></tr>
## <tr><td style="text-align:left">Desv. Pad.</td><td>19.072</td><td>4.709</td><td>1.855</td><td>21.679</td><td>3.431</td></tr>
## <tr><td colspan="6" style="border-bottom: 1px solid black"></td></tr></table>
# Junta o swap com a selic
selic_trim <- ts(selic_final[1:44], start = c(1996, 01, 01), frequency = 12)
# Binding the series
comb <- ts.union(selic_trim, swap90)
swap <- pmin(comb[,1], comb[,2], na.rm = TRUE)
#Inflação - Produto - Juros - Câmbio - Desigualdade.
var1 <- cbind(capital_trabalho_final*100, ipca, PIB*100, swap, cambio) # The bvar function does not allows data.frames
#var2 <- cbind(capital_trabalho_final, swap, PIB2, cambio, ipca) # The bvar function does not allows data.frames
names(var1) <- c("capital_trabalho", "ipca", "pib", "swap", "cambio")
#names(var1) <- c("ipca", "pib", "swap", "cambio","capital_trabalho") # Ficou uma merda
#var1 <- c(1,2,3,4,5)
pos_ct <- grep("capital_trabalho", names(var1))
pos_swap <- grep("swap", names(var1))
pos_pib <- grep("pib", names(var1))
pos_cambio <- grep("cambio", names(var1))
pos_ipca <- grep("ipca", names(var1))
set.seed(6969)
nburn. <- 1000000 # Burn the first 100kk replications
nrep. <- 100000 # Estimate another 100k times after burn in
thinfac. <- 4 # But keep only 1 in 4 estimates
p. <- 1 # Number of lags
tau. <- 48 - p. # Number of observations to use as prior
nf. <- 1 # Number of forecast periods
k_B. <- 6 # Fator de inflação na priori
k_A. <- 4 # Fator de inflação na priori
# No idea what's this for
tamanho <- floor(1/thinfac.*nrep.)
# número de tempos
tempo <- nrow(var1)
pm <- proc.time()
#fit1 <- bvar.sv.tvp(var1, p=p., tau = tau., nburn = nburn., nrep = nrep., thinfac = thinfac., nf = nf., k_B = k_B., k_A = k_A.)
#saveRDS(fit1, "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Testes\\fit.rds")
fit1 <- readRDS("D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Testes\\fit.rds")
#rm(fit1, ira)
proc.time() - pm
## user system elapsed
## 17.89 1.14 19.37
Caso queira ver qual a priori, descomente esses blocos de código (que estão ocultos).
Peguei a explicação daqui daqui: A FIR estima o impacto de um choque unitário em algum elemento de \(\varepsilon_t\). Os elementos de \(c_t\), \(B_{j,t}\) e \(A_t\) em (1) são mantidos fixos em seus valores em \(t\), mas os elementos de \(\Sigma_t\) são substituídos pela média de todos os períodos. Note que a ordem das variáveis importa e deve ser justificada por argumentos econômicos. As FIR contém os percentis 5, 25, 50, 75 e 95.
Na razão capital trabalho porém em períodos de mudança no Banco Central.
Os presidentes do BCB no período analisado foram:
Supondo que existe algum tipo de coordenação entre política fiscal e monetária, peguei os Ministros da Fazenda no Período também:
Os gráficos abaixo contém os betas (esq) e volatilidade (dir) ao longo do tempo, com o 16o e o 68o percentis (como foi feito no artigo do Primiceri).
Coeficiente (da própria variável defasada) e desvio padrão do resíduo, usando a média e os quantis 16 e 84 (os mesmos do primiceri) - esquerda - e mesmo gráfico, porém com o intervalo entre o 5 e 95 (área azul) quantis e 25 e 75 quantis (área cinza):
Coeficiente (da própria variável defasada) e desvio padrão do resíduo, usando a média e os quantis 16 e 84 (os mesmos do primiceri) - primeira coluna - e mesmo gráfico, porém com o intervalo entre o 5 e 95 (área azul) quantis e 25 e 75 quantis (área cinza) - segunda coluna. Também coloquei um gráfico do coeficiente com a escala vertical incluindo o zero - terceira coluna - para dar comparabilidade:
Coeficiente (da própria variável defasada) e desvio padrão do resíduo, usando a média e os quantis 16 e 84 (os mesmos do primiceri) - primeira coluna - e mesmo gráfico, porém com o intervalo entre o 5 e 95 (área azul) quantis e 25 e 75 quantis (área cinza) - segunda coluna. Também coloquei um gráfico do coeficiente com a escala vertical incluindo o zero - terceira coluna - para dar comparabilidade:
Coeficiente (da própria variável defasada) e desvio padrão do resíduo, usando a média e os quantis 16 e 84 (os mesmos do primiceri) - primeira coluna - e mesmo gráfico, porém com o intervalo entre o 5 e 95 (área azul) quantis e 25 e 75 quantis (área cinza) - segunda coluna. Também coloquei um gráfico do coeficiente com a escala vertical incluindo o zero - terceira coluna - para dar comparabilidade:
Coeficiente (da própria variável defasada) e desvio padrão do resíduo, usando a média e os quantis 16 e 84 (os mesmos do primiceri) - primeira coluna - e mesmo gráfico, porém com o intervalo entre o 5 e 95 (área azul) quantis e 25 e 75 quantis (área cinza) - segunda coluna. Também coloquei um gráfico do coeficiente com a escala vertical incluindo o zero - terceira coluna - para dar comparabilidade:
Primeiro, plotando os gráficos com o intervalo do 16o ao 84o quantil (como feito no Primiceri e como eu fiz no trabalho de Macro2:
Mas o que acontece se incluímos o zero no eixo vertical dos coeficientes?
Agora vamos repetir gráfico mas fazendo as bandas do quantil 5 a 95 (em azul) e 25 a 75 (em cinza) - sem forçar o zero no eixo dos coeficientes:
# Gráfico dos coeficientes das outras variáveis defasadas na equação da razão capital trabalho
x6beta_swap_ct <- t(apply(beta_swap_ct, 2, stat.helper))
x6beta_pib_ct <- t(apply(beta_pib_ct, 2, stat.helper))
x6beta_cambio_ct <- t(apply(beta_cambio_ct, 2, stat.helper))
x6beta_ipca_ct <- t(apply(beta_ipca_ct, 2, stat.helper))
# Novo Gráfico - coeficientes
df <- data.frame(Data2, x6beta_swap_ct, x6beta_pib_ct, x6beta_cambio_ct, x6beta_ipca_ct)
names(df) <- c("Data", "p16swap", "swap", "p84swap",
"p16pib", "pib", "p84pib",
"p16cambio", "cambio", "p84cambio",
"p16ipca", "ipca", "p84ipca")
graph_beta_swap_ct <- ggplot(data = df, aes(Data,swap)) +
geom_line(aes(y = p16swap), colour = cols1[2], linetype = "dashed") +
geom_line(aes(y = p84swap), colour = cols1[2], linetype = "dashed")+
geom_line(aes(y = swap), colour = 'skyblue4', size = 0.25)+
geom_ribbon(aes(x=Data, ymax=swap, ymin=p16swap), fill= cols1[1], alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p84swap, ymin=swap), fill= cols1[1], alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do Swap defasado na equação da Razão Capital-Trabalho (IC de 16 a 64)") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
#geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
graph_beta_swap_ct_alt <- ggplot(data = df, aes(Data,swap)) +
geom_line(aes(y = p16swap), colour = cols1[2], linetype = "dashed") +
geom_line(aes(y = p84swap), colour = cols1[2], linetype = "dashed")+
geom_line(aes(y = swap), colour = 'skyblue4', size = 0.25)+
geom_ribbon(aes(x=Data, ymax=swap, ymin=p16swap), fill= cols1[1], alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p84swap, ymin=swap), fill= cols1[1], alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do Swap defasado na equação da Razão Capital-Trabalho (IC de 16 a 64)") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
##
graph_beta_pib_ct <- ggplot(data = df, aes(Data,pib)) +
geom_line(aes(y = p16pib), colour = cols1[2], linetype = "dashed") +
geom_line(aes(y = p84pib), colour = cols1[2], linetype = "dashed")+
geom_line(aes(y = pib), colour = 'skyblue4', size = 0.25)+
geom_ribbon(aes(x=Data, ymax=pib, ymin=p16pib), fill= cols1[1], alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p84pib, ymin=pib), fill= cols1[1], alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do PIB defasado na equação da Razão Capital-Trabalho (IC de 16 a 64)") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
#geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
graph_beta_pib_ct_alt <- ggplot(data = df, aes(Data,pib)) +
geom_line(aes(y = p16pib), colour = cols1[2], linetype = "dashed") +
geom_line(aes(y = p84pib), colour = cols1[2], linetype = "dashed")+
geom_line(aes(y = pib), colour = 'skyblue4', size = 0.25)+
geom_ribbon(aes(x=Data, ymax=pib, ymin=p16pib), fill= cols1[1], alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p84pib, ymin=pib), fill= cols1[1], alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do PIB defasado na equação da Razão Capital-Trabalho (IC de 16 a 64)") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
##
graph_beta_cambio_ct <- ggplot(data = df, aes(Data,cambio)) +
geom_line(aes(y = p16cambio), colour = cols1[2], linetype = "dashed") +
geom_line(aes(y = p84cambio), colour = cols1[2], linetype = "dashed")+
geom_line(aes(y = cambio), colour = 'skyblue4', size = 0.25)+
geom_ribbon(aes(x=Data, ymax=cambio, ymin=p16cambio), fill= cols1[1], alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p84cambio, ymin=cambio), fill= cols1[1], alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do Câmbio defasado na equação da Razão Capital-Trabalho (IC de 16 a 64)") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
#geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
graph_beta_cambio_ct_alt <- ggplot(data = df, aes(Data,swap)) +
geom_line(aes(y = p16cambio), colour = cols1[2], linetype = "dashed") +
geom_line(aes(y = p84cambio), colour = cols1[2], linetype = "dashed")+
geom_line(aes(y = cambio), colour = 'skyblue4', size = 0.25)+
geom_ribbon(aes(x=Data, ymax=cambio, ymin=p16cambio), fill= cols1[1], alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p84cambio, ymin=cambio), fill= cols1[1], alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do Câmbio defasado na equação da Razão Capital-Trabalho (IC de 16 a 64)") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
##
graph_beta_ipca_ct <- ggplot(data = df, aes(Data,ipca)) +
geom_line(aes(y = p16ipca), colour = cols1[2], linetype = "dashed") +
geom_line(aes(y = p84ipca), colour = cols1[2], linetype = "dashed")+
geom_line(aes(y = ipca), colour = 'skyblue4', size = 0.25)+
geom_ribbon(aes(x=Data, ymax=ipca, ymin=p16ipca), fill= cols1[1], alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p84ipca, ymin=ipca), fill= cols1[1], alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do IPCA defasado na equação da Razão Capital-Trabalho (IC de 16 a 64)") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
#geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
graph_beta_ipca_ct_alt <- ggplot(data = df, aes(Data,ipca)) +
geom_line(aes(y = p16ipca), colour = cols1[2], linetype = "dashed") +
geom_line(aes(y = p84ipca), colour = cols1[2], linetype = "dashed")+
geom_line(aes(y = ipca), colour = 'skyblue4', size = 0.25)+
geom_ribbon(aes(x=Data, ymax=ipca, ymin=p16ipca), fill= cols1[1], alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p84ipca, ymin=ipca), fill= cols1[1], alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do IPCA defasado na equação da Razão Capital-Trabalho (IC de 16 a 64)") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
# Agora fazendo com os intervalos mais amplos
x6beta_swap_ct2 <- t(apply(beta_swap_ct, 2, stat.helper2))
x6beta_pib_ct2 <- t(apply(beta_pib_ct, 2, stat.helper2))
x6beta_cambio_ct2 <- t(apply(beta_cambio_ct, 2, stat.helper2))
x6beta_ipca_ct2 <- t(apply(beta_ipca_ct, 2, stat.helper2))
df2 <- data.frame(Data2, x6beta_swap_ct2)
names(df2) <- c("Data", "p5", "p25", "media", "p75", "p95")
graph_beta_swap_ct2 <- ggplot(data = df2, aes(Data,media)) +
geom_line(aes(y = p5), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = p25), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p75), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p95), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = media), size = 0.25)+
geom_ribbon(aes(x=Data, ymax=p25, ymin=p5), fill="skyblue3", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=media, ymin=p25), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p75, ymin=media), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p95, ymin=p75), fill="skyblue3", alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do Swap na equação da Razão Capital-Trabalho") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
#geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
graph_beta_swap_ct2_alt <- ggplot(data = df2, aes(Data,media)) +
geom_line(aes(y = p5), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = p25), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p75), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p95), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = media), size = 0.25)+
geom_ribbon(aes(x=Data, ymax=p25, ymin=p5), fill="skyblue3", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=media, ymin=p25), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p75, ymin=media), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p95, ymin=p75), fill="skyblue3", alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do Swap na equação da Razão Capital-Trabalho") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
df2 <- data.frame(Data2, x6beta_pib_ct2)
names(df2) <- c("Data", "p5", "p25", "media", "p75", "p95")
graph_beta_pib_ct2 <- ggplot(data = df2, aes(Data,media)) +
geom_line(aes(y = p5), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = p25), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p75), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p95), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = media), size = 0.25)+
geom_ribbon(aes(x=Data, ymax=p25, ymin=p5), fill="skyblue3", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=media, ymin=p25), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p75, ymin=media), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p95, ymin=p75), fill="skyblue3", alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do PIB na equação da Razão Capital-Trabalho") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
#geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
graph_beta_pib_ct2_alt <- ggplot(data = df2, aes(Data,media)) +
geom_line(aes(y = p5), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = p25), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p75), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p95), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = media), size = 0.25)+
geom_ribbon(aes(x=Data, ymax=p25, ymin=p5), fill="skyblue3", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=media, ymin=p25), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p75, ymin=media), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p95, ymin=p75), fill="skyblue3", alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do PIB na equação da Razão Capital-Trabalho") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
df2 <- data.frame(Data2, x6beta_cambio_ct2)
names(df2) <- c("Data", "p5", "p25", "media", "p75", "p95")
graph_beta_cambio_ct2 <- ggplot(data = df2, aes(Data,media)) +
geom_line(aes(y = p5), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = p25), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p75), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p95), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = media), size = 0.25)+
geom_ribbon(aes(x=Data, ymax=p25, ymin=p5), fill="skyblue3", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=media, ymin=p25), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p75, ymin=media), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p95, ymin=p75), fill="skyblue3", alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do Câmbio na equação da Razão Capital-Trabalho") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
#geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
graph_beta_cambio_ct2_alt <- ggplot(data = df2, aes(Data,media)) +
geom_line(aes(y = p5), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = p25), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p75), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p95), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = media), size = 0.25)+
geom_ribbon(aes(x=Data, ymax=p25, ymin=p5), fill="skyblue3", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=media, ymin=p25), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p75, ymin=media), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p95, ymin=p75), fill="skyblue3", alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do Câmbio na equação da Razão Capital-Trabalho") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
df2 <- data.frame(Data2, x6beta_ipca_ct2)
names(df2) <- c("Data", "p5", "p25", "media", "p75", "p95")
graph_beta_ipca_ct2 <- ggplot(data = df2, aes(Data,media)) +
geom_line(aes(y = p5), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = p25), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p75), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p95), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = media), size = 0.25)+
geom_ribbon(aes(x=Data, ymax=p25, ymin=p5), fill="skyblue3", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=media, ymin=p25), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p75, ymin=media), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p95, ymin=p75), fill="skyblue3", alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do IPCA na equação da Razão Capital-Trabalho") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
#geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
graph_beta_ipca_ct2_alt <- ggplot(data = df2, aes(Data,media)) +
geom_line(aes(y = p5), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = p25), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p75), colour = 'skyblue4', linetype = "longdash")+
geom_line(aes(y = p95), colour = 'skyblue3', linetype = "dashed") +
geom_line(aes(y = media), size = 0.25)+
geom_ribbon(aes(x=Data, ymax=p25, ymin=p5), fill="skyblue3", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=media, ymin=p25), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p75, ymin=media), fill="skyblue4", alpha=.3) +
geom_ribbon(aes(x=Data, ymax=p95, ymin=p75), fill="skyblue3", alpha=.3) +
xlab("Data") + ylab("Coeficiente") + ggtitle("Coeficiente do IPCA na equação da Razão Capital-Trabalho") +
scale_y_continuous(breaks = number_ticks(10)) +
scale_x_date(breaks = Data2[datemarks], name = "Data", labels = date_format("%Y"))+
geom_hline(yintercept = 0, size=0.5)+
mytheme_baixo2
Primeiro os gráficos com os intervalos de 16 a 84% sem forçar o zero no eixo y:
Agora o mesmo gráfico mas forçando o zero a aparecer:
E o mesmo gráfico mas com os quantis de 5 a 95 e 25 a 75:
Repete o mesmo de antes, mas incluindo zero no eixo y:
Estou me baseando nos seguintes linkis: * www.patricklam.org/teaching/convergence_print.pdf para traceplot, density plot, running mean plot (é o plot da iteração contra a média das observações até a iteração (ele está indo de 10 em 10 para frente na média)) * https://theoreticalecology.wordpress.com/2011/12/09/mcmc-chain-analysis-and-convergence-diagnostics-with-coda-in-r/
Um dos diagnósticos é plotar a cadeia (usando plot(mcmc_object)). Ele retorna o gráfico dos valores (um gráfico de linha - quanto mais ruidoso melhor) e um traceplot que é o gráfico da distribuição. Se eu não estou enganada, os meus Betas tem distribuição à posteriori normal e falta ver a distribuição dos sigmas. Se a densidade das matrizes é inversa wishart eles tem distribuição gamma, mas acho que não tem fórmula fechada para \(\Sigma\) - preciso ver no artigo do Primeri depois.
Outro diagnóstico das médias envolve fazer o gráfico da média usando uma janela móvel para ver se a posteriori cai em alguma região e fica empacada.
Como eu tenho muitos instantes de tempo (e portanto uma quantidade enorme de betas e de sigmas), eu selecionei arbitrariamente 15 betas (que é a divisão inteira de t por 10 - então estou plotando 10% dos parâmetros para cada \(y\)). Esses gráficos eu resolvi deixar de fora do artigo.
## [1] 190
## [1] 190
## [1] 190
## [1] 190
## [1] 190
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Agora tem o cumuplot() que faz o gráfico dos quantis da cadeia (de forma acumulada). O default é 0.025, 0.5, 0.975. Se eu tiver tempo depois, vou mexer no layout desses gráficos pois são feiosos demais. Também deixei de fora.
Por fim, tem o diagnóstico do Geweke, que calcula uma estatística com distribuição normal e que compara o início e o final da distribuição. De novo vou plotar só uma parte para não ficar muito grande. E deixei de fora do artigo
O bloco abaixo eu montei para entender melhor o que a autocorr() do pacote coda faz. No fim, vou ficar com a função de autocorrelação (não a parcial) pois ela avalia o efeito até o instante j. (o bloco agora está oculto)
Agora estou calculando a função te autocorrelação para depois fazer uns fancy graphs. O bloco do código está oculto.
## user system elapsed
## 107.91 0.00 107.98
Agora vamos para os gráficos…. a ideia é fazer algo como o Primiceri tem no anexo B (figura 9 - topo), porém dividindo por variável do VAR.
A estatística de Gelman-Rubin mede se há diferença significativa entre a variância dentro e entre diversas cadeias utilizando um fator de redução de escala. Aqui eu optei por simular duas cadeias e fazer a comparação entre elas. Em função da memória do computador eu utilizei um número menor de iterações salvas: ao invés de salvar todos os valores, armazenei apenas os 10.000 últimos valores (20%).
## user system elapsed
## 17.42 1.10 20.53
## $psrf
## Point est. Upper C.I.
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## [441,] 1.0004481 1.0022618
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## [443,] 1.0004945 1.0025183
## [444,] 1.0004760 1.0024330
## [445,] 1.0004936 1.0025437
## [446,] 1.0005130 1.0026153
## [447,] 1.0005389 1.0027543
## [448,] 1.0005169 1.0026473
## [449,] 1.0005506 1.0028210
## [450,] 1.0005281 1.0027153
## [451,] 1.0005113 1.0026413
## [452,] 1.0004574 1.0023637
## [453,] 1.0004392 1.0022692
## [454,] 1.0004647 1.0023863
## [455,] 1.0004715 1.0023983
## [456,] 1.0004714 1.0023913
## [457,] 1.0004721 1.0023761
## [458,] 1.0004824 1.0024004
## [459,] 1.0004442 1.0021991
## [460,] 1.0004338 1.0021326
## [461,] 1.0004460 1.0021827
## [462,] 1.0004428 1.0021231
## [463,] 1.0004366 1.0021020
## [464,] 1.0004585 1.0022236
## [465,] 1.0004384 1.0021448
## [466,] 1.0004440 1.0021517
## [467,] 1.0004882 1.0023478
## [468,] 1.0005044 1.0024519
## [469,] 1.0005230 1.0024956
## [470,] 1.0005309 1.0025527
## [471,] 1.0005112 1.0024480
## [472,] 1.0005051 1.0023756
## [473,] 1.0005179 1.0024270
## [474,] 1.0005138 1.0023864
## [475,] 1.0005292 1.0024702
## [476,] 1.0005467 1.0025180
## [477,] 1.0005387 1.0024899
## [478,] 1.0005427 1.0025416
## [479,] 1.0005442 1.0025027
## [480,] 1.0005532 1.0025491
## [481,] 1.0005632 1.0025898
## [482,] 1.0005947 1.0026716
## [483,] 1.0006035 1.0026689
## [484,] 1.0006165 1.0027713
## [485,] 1.0006069 1.0027222
## [486,] 1.0006148 1.0027868
## [487,] 1.0006510 1.0030352
## [488,] 1.0006598 1.0030372
## [489,] 1.0006955 1.0031570
## [490,] 1.0007122 1.0032418
## [491,] 1.0007143 1.0032644
## [492,] 1.0007192 1.0033095
## [493,] 1.0007387 1.0034424
## [494,] 1.0007767 1.0036157
## [495,] 1.0008188 1.0038402
## [496,] 1.0008383 1.0039905
## [497,] 1.0008595 1.0040867
## [498,] 1.0008791 1.0041615
## [499,] 1.0009114 1.0042584
## [500,] 1.0008748 1.0041007
## [501,] 1.0008601 1.0040360
## [502,] 1.0008171 1.0038573
## [503,] 1.0007819 1.0037200
## [504,] 1.0007551 1.0035409
## [505,] 1.0007559 1.0034797
## [506,] 1.0006961 1.0031818
## [507,] 1.0006833 1.0030939
## [508,] 1.0006843 1.0030791
## [509,] 1.0006845 1.0030348
## [510,] 1.0006781 1.0030134
## [511,] 1.0006947 1.0030731
## [512,] 1.0006619 1.0029078
## [513,] 1.0006438 1.0028224
## [514,] 1.0006608 1.0028793
## [515,] 1.0006214 1.0027546
## [516,] 1.0005967 1.0026885
## [517,] 1.0005914 1.0026577
## [518,] 1.0005697 1.0025431
## [519,] 1.0005750 1.0025379
## [520,] 1.0005836 1.0025589
## [521,] 1.0005978 1.0026042
## [522,] 1.0005870 1.0025262
## [523,] 1.0005765 1.0024577
## [524,] 1.0005939 1.0024920
## [525,] 1.0006184 1.0025723
## [526,] 1.0006004 1.0024752
## [527,] 1.0006181 1.0025157
## [528,] 1.0005709 1.0022797
## [529,] 1.0005167 1.0020766
## [530,] 1.0004957 1.0019072
## [531,] 1.0004823 1.0017846
## [532,] 1.0004998 1.0018364
## [533,] 1.0004835 1.0016688
## [534,] 1.0004710 1.0015493
## [535,] 1.0004393 1.0014035
## [536,] 1.0004299 1.0012830
## [537,] 1.0004302 1.0012457
## [538,] 1.0004436 1.0013276
## [539,] 1.0004401 1.0012983
## [540,] 1.0004215 1.0013094
## [541,] 1.0004438 1.0013589
## [542,] 1.0004321 1.0013458
## [543,] 1.0004744 1.0014751
## [544,] 1.0005007 1.0015528
## [545,] 1.0005028 1.0015951
## [546,] 1.0005156 1.0016174
## [547,] 1.0005029 1.0016460
## [548,] 1.0004830 1.0016095
## [549,] 1.0004919 1.0016413
## [550,] 1.0004907 1.0017051
## [551,] 1.0005026 1.0017674
## [552,] 1.0004757 1.0017120
## [553,] 1.0004789 1.0017286
## [554,] 1.0005011 1.0018003
## [555,] 1.0005217 1.0018516
## [556,] 1.0004733 1.0016894
## [557,] 1.0004506 1.0016115
## [558,] 1.0004185 1.0014636
## [559,] 1.0004191 1.0014454
## [560,] 1.0004116 1.0014023
## [561,] 1.0004225 1.0014328
## [562,] 1.0004744 1.0016147
## [563,] 1.0004954 1.0017467
## [564,] 1.0005321 1.0018837
## [565,] 1.0005430 1.0019106
## [566,] 1.0005479 1.0019221
## [567,] 1.0005677 1.0019474
## [568,] 1.0005767 1.0020274
## [569,] 1.0006256 1.0022721
## [570,] 1.0006323 1.0023359
## [571,] 1.0006669 1.0025964
## [572,] 1.0006814 1.0028014
## [573,] 1.0007202 1.0029961
## [574,] 1.0007998 1.0033550
## [575,] 1.0008645 1.0037388
## [576,] 1.0009715 1.0042658
## [577,] 1.0010986 1.0048596
## [578,] 1.0011817 1.0052628
## [579,] 1.0012516 1.0056097
## [580,] 1.0012788 1.0057762
## [581,] 1.0013200 1.0059820
## [582,] 1.0013776 1.0063133
## [583,] 1.0014115 1.0065506
## [584,] 1.0014338 1.0066798
## [585,] 1.0014045 1.0064968
## [586,] 1.0013457 1.0062069
## [587,] 1.0013290 1.0060999
## [588,] 1.0012804 1.0058252
## [589,] 1.0012685 1.0056923
## [590,] 1.0012251 1.0055060
## [591,] 1.0012287 1.0055533
## [592,] 1.0012259 1.0055489
## [593,] 1.0012086 1.0054035
## [594,] 1.0011803 1.0053276
## [595,] 1.0011808 1.0052437
## [596,] 1.0011301 1.0049915
## [597,] 1.0010632 1.0046567
## [598,] 1.0010872 1.0047145
## [599,] 1.0010564 1.0046031
## [600,] 1.0010067 1.0043953
## [601,] 1.0010006 1.0043802
## [602,] 1.0009824 1.0043231
## [603,] 1.0009694 1.0043317
## [604,] 1.0009446 1.0042473
## [605,] 1.0009326 1.0041704
## [606,] 1.0009837 1.0044248
## [607,] 1.0009426 1.0042744
## [608,] 1.0010031 1.0045646
## [609,] 1.0010210 1.0046545
## [610,] 1.0010093 1.0046236
## [611,] 1.0009943 1.0045853
## [612,] 1.0009971 1.0045693
## [613,] 1.0009312 1.0042756
## [614,] 1.0009249 1.0042229
## [615,] 1.0009227 1.0041536
## [616,] 1.0008938 1.0039941
## [617,] 1.0008953 1.0039870
## [618,] 1.0009328 1.0041202
## [619,] 1.0009368 1.0041289
## [620,] 1.0009315 1.0040742
## [621,] 1.0009670 1.0042488
## [622,] 1.0009250 1.0041552
## [623,] 1.0009877 1.0043866
## [624,] 1.0010154 1.0045257
## [625,] 1.0010747 1.0047593
## [626,] 1.0010911 1.0048958
## [627,] 1.0011351 1.0051436
## [628,] 1.0011517 1.0052302
## [629,] 1.0011773 1.0053435
## [630,] 1.0012159 1.0055090
## [631,] 1.0012978 1.0059245
## [632,] 1.0013180 1.0060433
## [633,] 1.0013322 1.0061741
## [634,] 1.0013480 1.0063254
## [635,] 1.0014166 1.0066682
## [636,] 1.0014432 1.0068448
## [637,] 1.0015024 1.0071847
## [638,] 1.0016001 1.0076743
## [639,] 1.0016661 1.0080062
## [640,] 1.0017462 1.0084796
## [641,] 1.0018092 1.0088220
## [642,] 1.0018909 1.0092536
## [643,] 1.0019551 1.0095544
## [644,] 1.0019497 1.0095274
## [645,] 1.0019312 1.0094410
## [646,] 1.0019501 1.0094963
## [647,] 1.0020316 1.0099152
## [648,] 1.0019767 1.0096998
## [649,] 1.0019408 1.0095005
## [650,] 1.0019044 1.0093045
## [651,] 1.0018828 1.0092095
## [652,] 1.0018783 1.0091877
## [653,] 1.0017929 1.0087848
## [654,] 1.0017860 1.0086938
## [655,] 1.0021302 1.0106395
## [656,] 1.0020943 1.0104407
## [657,] 1.0020966 1.0104262
## [658,] 1.0020621 1.0102809
## [659,] 1.0020298 1.0100754
## [660,] 1.0019838 1.0098954
## [661,] 1.0019462 1.0097176
## [662,] 1.0019695 1.0098119
## [663,] 1.0018991 1.0094826
## [664,] 1.0018544 1.0092790
## [665,] 1.0017934 1.0089550
## [666,] 1.0018606 1.0092509
## [667,] 1.0017998 1.0089638
## [668,] 1.0017391 1.0086457
## [669,] 1.0017542 1.0086440
## [670,] 1.0016821 1.0082630
## [671,] 1.0016819 1.0082523
## [672,] 1.0016716 1.0082383
## [673,] 1.0016321 1.0080917
## [674,] 1.0016570 1.0082208
## [675,] 1.0016862 1.0083660
## [676,] 1.0016489 1.0081727
## [677,] 1.0016209 1.0080605
## [678,] 1.0016052 1.0079977
## [679,] 1.0015325 1.0076565
## [680,] 1.0014803 1.0074075
## [681,] 1.0013669 1.0068366
## [682,] 1.0013866 1.0069310
## [683,] 1.0013966 1.0069996
## [684,] 1.0013862 1.0069193
## [685,] 1.0013800 1.0069126
## [686,] 1.0013770 1.0069317
## [687,] 1.0013804 1.0069199
## [688,] 1.0014367 1.0071934
## [689,] 1.0013656 1.0068438
## [690,] 1.0014375 1.0072027
## [691,] 1.0014875 1.0074190
## [692,] 1.0015010 1.0074741
## [693,] 1.0015968 1.0079426
## [694,] 1.0017218 1.0085046
## [695,] 1.0017957 1.0089175
## [696,] 1.0018346 1.0091304
## [697,] 1.0019070 1.0095240
## [698,] 1.0018620 1.0093498
## [699,] 1.0017847 1.0089891
## [700,] 1.0018649 1.0093665
## [701,] 1.0018607 1.0093397
## [702,] 1.0018167 1.0091426
## [703,] 1.0018011 1.0090501
## [704,] 1.0017555 1.0088473
## [705,] 1.0017037 1.0086109
## [706,] 1.0016724 1.0084540
## [707,] 1.0016102 1.0081423
## [708,] 1.0016066 1.0080968
## [709,] 1.0015322 1.0077489
## [710,] 1.0014620 1.0073836
## [711,] 1.0013823 1.0070250
## [712,] 1.0012527 1.0063898
## [713,] 1.0012071 1.0061576
## [714,] 1.0012013 1.0061193
## [715,] 1.0011909 1.0060827
## [716,] 1.0011699 1.0059764
## [717,] 1.0011607 1.0059304
## [718,] 1.0012090 1.0061683
## [719,] 1.0013088 1.0066683
## [720,] 1.0013506 1.0068752
## [721,] 1.0014327 1.0072947
## [722,] 1.0015973 1.0081168
## [723,] 1.0017664 1.0089475
## [724,] 1.0019452 1.0098193
## [725,] 1.0020590 1.0103720
## [726,] 1.0021128 1.0106187
## [727,] 1.0020853 1.0104420
## [728,] 1.0021104 1.0105183
## [729,] 1.0021317 1.0106126
## [730,] 1.0021013 1.0104369
## [731,] 1.0021253 1.0105469
## [732,] 1.0021009 1.0104490
## [733,] 1.0020703 1.0102470
## [734,] 1.0020798 1.0102425
## [735,] 1.0020785 1.0102153
## [736,] 1.0020182 1.0099229
## [737,] 1.0018838 1.0092943
## [738,] 1.0017897 1.0088006
## [739,] 1.0017358 1.0085342
## [740,] 1.0017932 1.0088246
## [741,] 1.0017590 1.0087085
## [742,] 1.0018013 1.0088966
## [743,] 1.0018494 1.0090897
## [744,] 1.0017756 1.0087335
## [745,] 1.0017581 1.0086317
## [746,] 1.0017401 1.0085595
## [747,] 1.0016188 1.0079313
## [748,] 1.0014963 1.0074063
## [749,] 1.0014577 1.0071886
## [750,] 1.0014355 1.0070450
## [751,] 1.0013812 1.0068019
## [752,] 1.0013484 1.0066815
## [753,] 1.0012201 1.0060657
## [754,] 1.0011583 1.0058158
## [755,] 1.0011873 1.0059668
## [756,] 1.0012274 1.0061846
## [757,] 1.0012466 1.0062638
## [758,] 1.0013277 1.0066058
## [759,] 1.0014501 1.0071777
## [760,] 1.0016835 1.0081955
## [761,] 1.0018169 1.0087486
## [762,] 1.0019828 1.0094979
## [763,] 1.0021122 1.0101739
## [764,] 1.0023173 1.0111667
## [765,] 1.0023282 1.0111680
## [766,] 1.0021895 1.0104647
## [767,] 1.0021545 1.0103867
## [768,] 1.0021425 1.0103905
## [769,] 1.0021077 1.0102480
## [770,] 1.0019976 1.0096773
## [771,] 1.0019645 1.0095148
## [772,] 1.0019367 1.0094516
## [773,] 1.0018996 1.0093018
## [774,] 1.0018156 1.0088270
## [775,] 1.0017307 1.0084120
## [776,] 1.0016034 1.0077449
## [777,] 1.0015023 1.0072992
## [778,] 1.0013514 1.0066207
## [779,] 1.0013850 1.0067391
## [780,] 1.0014362 1.0069914
## [781,] 1.0015929 1.0076373
## [782,] 1.0016715 1.0079193
## [783,] 1.0017633 1.0083253
## [784,] 1.0017473 1.0083738
## [785,] 1.0016636 1.0079930
## [786,] 1.0016703 1.0080608
## [787,] 1.0016837 1.0081531
## [788,] 1.0018064 1.0088075
## [789,] 1.0020002 1.0097924
## [790,] 1.0021676 1.0105518
## [791,] 1.0022767 1.0110671
## [792,] 1.0025083 1.0121715
## [793,] 1.0027364 1.0133258
## [794,] 1.0030716 1.0149253
## [795,] 1.0033156 1.0160656
## [796,] 1.0035638 1.0173144
## [797,] 1.0036727 1.0178642
## [798,] 1.0037353 1.0182542
## [799,] 1.0040483 1.0197080
## [800,] 1.0040044 1.0195452
## [801,] 1.0040978 1.0200877
## [802,] 1.0041206 1.0202194
## [803,] 1.0040230 1.0197526
## [804,] 1.0039486 1.0194051
## [805,] 1.0039144 1.0192753
## [806,] 1.0037501 1.0184862
## [807,] 1.0034592 1.0170984
## [808,] 1.0034351 1.0169586
## [809,] 1.0033160 1.0163817
## [810,] 1.0032738 1.0161668
## [811,] 1.0032759 1.0162305
## [812,] 1.0031283 1.0155347
## [813,] 1.0031060 1.0154292
## [814,] 1.0029356 1.0146173
## [815,] 1.0026909 1.0134516
## [816,] 1.0025972 1.0129877
## [817,] 1.0025220 1.0126110
## [818,] 1.0024751 1.0123562
## [819,] 1.0025229 1.0125818
## [820,] 1.0023989 1.0120151
## [821,] 1.0023098 1.0115943
## [822,] 1.0022766 1.0114510
## [823,] 1.0022023 1.0110894
## [824,] 1.0022585 1.0113582
## [825,] 1.0022113 1.0111267
## [826,] 1.0022881 1.0115082
## [827,] 1.0023522 1.0118164
## [828,] 1.0024577 1.0123321
## [829,] 1.0024601 1.0123534
## [830,] 1.0024039 1.0120826
## [831,] 1.0022277 1.0112199
## [832,] 1.0020560 1.0103768
## [833,] 1.0020420 1.0103084
## [834,] 1.0019618 1.0099088
## [835,] 1.0021039 1.0106050
## [836,] 1.0021264 1.0106955
## [837,] 1.0022219 1.0111691
## [838,] 1.0022638 1.0113799
## [839,] 1.0023076 1.0116026
## [840,] 1.0024070 1.0120763
## [841,] 1.0026453 1.0132586
## [842,] 1.0028923 1.0144582
## [843,] 1.0030742 1.0153388
## [844,] 1.0033280 1.0165708
## [845,] 1.0034609 1.0172112
## [846,] 1.0036907 1.0183260
## [847,] 1.0039971 1.0198091
## [848,] 1.0041562 1.0205782
## [849,] 1.0042653 1.0210955
## [850,] 1.0043452 1.0214703
## [851,] 1.0045133 1.0222924
## [852,] 1.0045224 1.0223328
## [853,] 1.0046510 1.0229459
## [854,] 1.0047950 1.0236432
## [855,] 1.0050043 1.0246573
## [856,] 1.0050452 1.0248466
## [857,] 1.0050641 1.0249265
## [858,] 1.0053059 1.0260593
## [859,] 1.0054038 1.0265206
## [860,] 1.0055454 1.0271860
## [861,] 1.0055780 1.0273019
## [862,] 1.0055339 1.0270942
## [863,] 1.0055692 1.0272631
## [864,] 1.0056414 1.0276148
## [865,] 1.0057901 1.0282966
## [866,] 1.0058093 1.0283952
## [867,] 1.0056225 1.0275309
## [868,] 1.0055538 1.0272292
## [869,] 1.0054139 1.0265218
## [870,] 1.0052744 1.0258688
## [871,] 1.0050732 1.0249290
## [872,] 1.0049824 1.0244913
## [873,] 1.0001834 1.0006014
## [874,] 1.0001884 1.0006131
## [875,] 1.0001861 1.0006074
## [876,] 1.0001794 1.0005915
## [877,] 1.0001780 1.0005880
## [878,] 1.0001743 1.0005850
## [879,] 1.0001780 1.0006074
## [880,] 1.0001698 1.0005773
## [881,] 1.0001747 1.0005977
## [882,] 1.0001751 1.0005916
## [883,] 1.0001728 1.0005866
## [884,] 1.0001730 1.0005691
## [885,] 1.0001777 1.0005893
## [886,] 1.0001863 1.0006059
## [887,] 1.0001862 1.0006083
## [888,] 1.0001933 1.0006172
## [889,] 1.0002044 1.0006535
## [890,] 1.0002031 1.0006649
## [891,] 1.0001992 1.0006369
## [892,] 1.0002063 1.0006332
## [893,] 1.0002120 1.0006422
## [894,] 1.0002085 1.0006310
## [895,] 1.0002092 1.0006264
## [896,] 1.0002052 1.0006282
## [897,] 1.0002052 1.0006250
## [898,] 1.0002164 1.0006471
## [899,] 1.0002173 1.0006349
## [900,] 1.0002276 1.0006595
## [901,] 1.0002238 1.0006468
## [902,] 1.0002289 1.0006916
## [903,] 1.0002277 1.0006962
## [904,] 1.0002339 1.0006951
## [905,] 1.0002393 1.0007191
## [906,] 1.0002352 1.0007098
## [907,] 1.0002339 1.0007094
## [908,] 1.0002270 1.0007025
## [909,] 1.0002231 1.0007013
## [910,] 1.0002200 1.0006760
## [911,] 1.0002126 1.0006558
## [912,] 1.0002149 1.0006461
## [913,] 1.0002079 1.0006217
## [914,] 1.0002079 1.0006252
## [915,] 1.0002099 1.0006240
## [916,] 1.0002167 1.0006340
## [917,] 1.0002214 1.0006653
## [918,] 1.0002271 1.0007045
## [919,] 1.0002285 1.0007086
## [920,] 1.0002300 1.0007124
## [921,] 1.0002243 1.0007126
## [922,] 1.0002203 1.0007012
## [923,] 1.0002250 1.0007277
## [924,] 1.0002289 1.0007327
## [925,] 1.0002226 1.0007020
## [926,] 1.0002158 1.0006766
## [927,] 1.0002195 1.0006866
## [928,] 1.0002276 1.0007139
## [929,] 1.0002292 1.0007247
## [930,] 1.0002287 1.0007240
## [931,] 1.0002192 1.0007022
## [932,] 1.0002154 1.0006848
## [933,] 1.0002173 1.0006857
## [934,] 1.0002148 1.0006918
## [935,] 1.0002221 1.0007296
## [936,] 1.0002262 1.0007391
## [937,] 1.0002286 1.0007594
## [938,] 1.0002352 1.0007795
## [939,] 1.0002376 1.0007941
## [940,] 1.0002369 1.0007850
## [941,] 1.0002313 1.0007959
## [942,] 1.0002311 1.0007868
## [943,] 1.0002275 1.0007779
## [944,] 1.0002301 1.0007885
## [945,] 1.0002325 1.0008153
## [946,] 1.0002375 1.0008198
## [947,] 1.0002287 1.0007838
## [948,] 1.0002233 1.0007554
## [949,] 1.0002195 1.0007278
## [950,] 1.0002236 1.0007318
## [951,] 1.0002175 1.0007115
## [952,] 1.0002053 1.0006745
## [953,] 1.0002010 1.0006621
## [954,] 1.0001944 1.0006371
## [955,] 1.0001935 1.0006295
## [956,] 1.0002001 1.0006582
## [957,] 1.0001970 1.0006675
## [958,] 1.0001932 1.0006431
## [959,] 1.0002023 1.0006645
## [960,] 1.0002011 1.0006548
## [961,] 1.0002026 1.0006537
## [962,] 1.0001920 1.0006289
## [963,] 1.0001973 1.0006288
## [964,] 1.0001970 1.0006469
## [965,] 1.0001922 1.0006339
## [966,] 1.0001839 1.0006008
## [967,] 1.0001773 1.0005755
## [968,] 1.0001811 1.0005960
## [969,] 1.0001874 1.0005961
## [970,] 1.0001954 1.0005955
## [971,] 1.0001818 1.0005652
## [972,] 1.0001801 1.0005705
## [973,] 1.0001740 1.0005403
## [974,] 1.0001741 1.0005432
## [975,] 1.0001777 1.0005581
## [976,] 1.0001862 1.0005764
## [977,] 1.0001984 1.0006043
## [978,] 1.0001941 1.0006197
## [979,] 1.0001981 1.0006356
## [980,] 1.0002053 1.0006494
## [981,] 1.0002081 1.0006668
## [982,] 1.0002116 1.0006776
## [983,] 1.0002154 1.0006939
## [984,] 1.0002138 1.0006917
## [985,] 1.0002113 1.0006916
## [986,] 1.0002122 1.0006960
## [987,] 1.0002095 1.0006955
## [988,] 1.0001977 1.0006579
## [989,] 1.0001964 1.0006432
## [990,] 1.0002003 1.0006635
## [991,] 1.0001992 1.0006951
## [992,] 1.0002022 1.0006949
## [993,] 1.0002073 1.0007012
## [994,] 1.0002053 1.0006723
## [995,] 1.0002030 1.0006450
## [996,] 1.0002065 1.0006428
## [997,] 1.0002041 1.0006375
## [998,] 1.0002070 1.0006483
## [999,] 1.0002074 1.0006569
## [1000,] 1.0002096 1.0006688
## [1001,] 1.0002122 1.0006876
## [1002,] 1.0002106 1.0006915
## [1003,] 1.0002151 1.0007129
## [1004,] 1.0002204 1.0007239
## [1005,] 1.0002245 1.0007307
## [1006,] 1.0002237 1.0007548
## [1007,] 1.0002289 1.0007858
## [1008,] 1.0002300 1.0007959
## [1009,] 1.0002316 1.0008105
## [1010,] 1.0002411 1.0008869
## [1011,] 1.0002382 1.0008871
## [1012,] 1.0002432 1.0009299
## [1013,] 1.0002600 1.0010043
## [1014,] 1.0002646 1.0010218
## [1015,] 1.0002776 1.0010825
## [1016,] 1.0002977 1.0011535
## [1017,] 1.0003087 1.0011852
## [1018,] 1.0003113 1.0011839
## [1019,] 1.0003309 1.0012639
## [1020,] 1.0003339 1.0012655
## [1021,] 1.0003355 1.0012881
## [1022,] 1.0003441 1.0012900
## [1023,] 1.0003415 1.0012805
## [1024,] 1.0003361 1.0012644
## [1025,] 1.0003235 1.0011918
## [1026,] 1.0003077 1.0011368
## [1027,] 1.0003034 1.0011220
## [1028,] 1.0003094 1.0011287
## [1029,] 1.0003132 1.0011209
## [1030,] 1.0003175 1.0011386
## [1031,] 1.0003192 1.0011529
## [1032,] 1.0003179 1.0011473
## [1033,] 1.0003143 1.0011372
## [1034,] 1.0003165 1.0011449
## [1035,] 1.0003014 1.0011018
## [1036,] 1.0002929 1.0010604
## [1037,] 1.0002869 1.0010227
## [1038,] 1.0002706 1.0009600
## [1039,] 1.0002717 1.0009598
## [1040,] 1.0002719 1.0009458
## [1041,] 1.0002698 1.0009448
## [1042,] 1.0002648 1.0009500
## [1043,] 1.0002591 1.0009421
## [1044,] 1.0002604 1.0009684
## [1045,] 1.0002727 1.0010124
## [1046,] 1.0002751 1.0010409
## [1047,] 1.0002757 1.0010556
## [1048,] 1.0002745 1.0010582
## [1049,] 1.0002770 1.0010593
## [1050,] 1.0002776 1.0010530
## [1051,] 1.0002774 1.0010773
## [1052,] 1.0002682 1.0010374
## [1053,] 1.0002726 1.0010732
## [1054,] 1.0002793 1.0010753
## [1055,] 1.0002778 1.0010732
## [1056,] 1.0002716 1.0010681
## [1057,] 1.0002757 1.0010896
## [1058,] 1.0002734 1.0010670
## [1059,] 1.0002777 1.0010800
## [1060,] 1.0002887 1.0010941
## [1061,] 1.0002888 1.0011054
## [1062,] 1.0002970 1.0011247
## [1063,] 1.0003129 1.0011840
## [1064,] 1.0003109 1.0011766
## [1065,] 1.0003010 1.0011423
## [1066,] 1.0003015 1.0011540
## [1067,] 1.0002994 1.0011724
## [1068,] 1.0003007 1.0011842
## [1069,] 1.0003112 1.0012299
## [1070,] 1.0003147 1.0012529
## [1071,] 1.0003190 1.0012844
## [1072,] 1.0003296 1.0013234
## [1073,] 1.0003382 1.0013780
## [1074,] 1.0003492 1.0014205
## [1075,] 1.0003683 1.0015054
## [1076,] 1.0003779 1.0015608
## [1077,] 1.0003753 1.0015859
## [1078,] 1.0003697 1.0015575
## [1079,] 1.0003765 1.0015820
## [1080,] 1.0003841 1.0016133
## [1081,] 1.0003927 1.0016777
## [1082,] 1.0003975 1.0016597
## [1083,] 1.0004041 1.0016715
## [1084,] 1.0004092 1.0016980
## [1085,] 1.0004117 1.0017127
## [1086,] 1.0004133 1.0017014
## [1087,] 1.0004209 1.0017217
## [1088,] 1.0004354 1.0017676
## [1089,] 1.0004205 1.0017111
## [1090,] 1.0004135 1.0016922
## [1091,] 1.0067203 1.0231532
## [1092,] 1.0024034 1.0024512
## [1093,] 1.0137925 1.0142605
## [1094,] 1.0071440 1.0079188
## [1095,] 1.0024637 1.0042140
## [1096,] 1.0008154 1.0011308
## [1097,] 1.0000145 1.0000312
## [1098,] 1.0002636 1.0008441
## [1099,] 1.0007814 1.0007815
## [1100,] 1.0002339 1.0007712
## [1101,] 1.0138697 1.0231166
## [1102,] 1.0027775 1.0121374
## [1103,] 1.0083250 1.0197085
## [1104,] 1.0317388 1.0464106
## [1105,] 1.0027661 1.0133047
## [1106,] 1.0016880 1.0082013
## [1107,] 1.0146295 1.0182647
## [1108,] 1.0099693 1.0106662
## [1109,] 1.0062589 1.0074730
## [1110,] 1.0023481 1.0041072
## [1111,] 1.0010721 1.0010722
## [1112,] 1.0143272 1.0159985
## [1113,] 1.0022779 1.0030475
## [1114,] 1.0003576 1.0014747
## [1115,] 1.0188363 1.0209113
## [1116,] 1.0017449 1.0021572
## [1117,] 1.0660538 1.0668254
## [1118,] 1.0100335 1.0100652
## [1119,] 1.0002525 1.0005526
## [1120,] 1.0029189 1.0070513
## [1121,] 1.1234176 1.1310356
## [1122,] 1.0064471 1.0106282
## [1123,] 1.0015744 1.0018217
## [1124,] 1.0040559 1.0046924
## [1125,] 1.0036362 1.0115126
## [1126,] 1.0127029 1.0339951
## [1127,] 1.0161177 1.0410420
## [1128,] 1.0029052 1.0142415
## [1129,] 1.0143876 1.0237120
## [1130,] 1.0510631 1.0563205
## [1131,] 1.0016849 1.0036017
## [1132,] 1.0019912 1.0020420
## [1133,] 1.0009330 1.0015449
## [1134,] 1.0004132 1.0006839
## [1135,] 1.0025940 1.0095782
## [1136,] 1.0345036 1.0579674
## [1137,] 1.0991484 1.1708777
## [1138,] 1.0759841 1.1369574
## [1139,] 1.0652357 1.1182179
## [1140,] 1.0292515 1.0553392
## [1141,] 1.0313657 1.0497816
## [1142,] 1.0017161 1.0083897
## [1143,] 1.0058174 1.0154029
## [1144,] 1.0015089 1.0061871
## [1145,] 1.0034609 1.0061164
## [1146,] 1.0030641 1.0054108
## [1147,] 1.0005131 1.0018607
## [1148,] 1.0019453 1.0029984
## [1149,] 1.0068476 1.0069798
## [1150,] 1.0004939 1.0021095
## [1151,] 1.0011182 1.0032606
## [1152,] 1.0016650 1.0028684
## [1153,] 1.0036836 1.0061960
## [1154,] 1.0034930 1.0087797
## [1155,] 1.0084141 1.0160235
## [1156,] 1.0137234 1.0227962
## [1157,] 1.0109940 1.0176574
## [1158,] 1.0032483 1.0120476
## [1159,] 1.0153546 1.0284053
## [1160,] 1.0068242 1.0143852
## [1161,] 1.0266006 1.0324909
## [1162,] 1.0088114 1.0189521
## [1163,] 1.0150486 1.0193931
## [1164,] 1.0390544 1.0535628
## [1165,] 1.0095739 1.0183392
## [1166,] 1.0053002 1.0142359
## [1167,] 1.0157465 1.0305594
## [1168,] 1.0121826 1.0182998
## [1169,] 1.0124175 1.0135075
## [1170,] 1.0162823 1.0203909
## [1171,] 1.0037295 1.0108076
## [1172,] 1.0056696 1.0164498
## [1173,] 1.0073727 1.0173004
## [1174,] 1.0047045 1.0076104
## [1175,] 1.0001231 1.0007656
## [1176,] 1.0040975 1.0042122
## [1177,] 1.0179518 1.0181979
## [1178,] 1.0015396 1.0017884
## [1179,] 1.0039391 1.0042011
## [1180,] 1.0002851 1.0009082
## [1181,] 1.0024488 1.0024761
## [1182,] 1.0002209 1.0008846
## [1183,] 1.0030863 1.0031416
## [1184,] 1.0024574 1.0029697
## [1185,] 1.0003040 1.0015913
## [1186,] 1.0089008 1.0096706
## [1187,] 1.0006350 1.0027719
## [1188,] 1.0509800 1.0595334
## [1189,] 1.0119790 1.0207840
## [1190,] 1.0056094 1.0090164
## [1191,] 1.0006715 1.0007132
## [1192,] 1.0078774 1.0081977
## [1193,] 1.0022624 1.0025122
## [1194,] 1.0014908 1.0017523
## [1195,] 1.0047249 1.0053444
## [1196,] 1.0108378 1.0131478
## [1197,] 1.0112368 1.0126275
## [1198,] 1.0247404 1.0247591
## [1199,] 1.0009965 1.0051336
## [1200,] 1.0407421 1.0594642
## [1201,] 1.0282226 1.0485175
## [1202,] 1.0485442 1.0614651
## [1203,] 1.0002335 1.0007255
## [1204,] 1.0001395 1.0002672
## [1205,] 1.0000750 1.0005249
## [1206,] 1.0189007 1.0189041
## [1207,] 1.0001160 1.0005391
## [1208,] 1.0000846 1.0003513
## [1209,] 1.0002795 1.0008283
## [1210,] 1.0004109 1.0014971
## [1211,] 1.0019429 1.0044994
## [1212,] 1.0025336 1.0097128
## [1213,] 1.0033011 1.0139992
## [1214,] 1.0230928 1.0605119
## [1215,] 1.0220211 1.0431762
## [1216,] 1.0031456 1.0104240
## [1217,] 1.0043782 1.0061869
## [1218,] 1.0000426 1.0001744
## [1219,] 1.0043267 1.0056221
## [1220,] 1.0055240 1.0112130
## [1221,] 1.0048407 1.0106512
## [1222,] 1.0126254 1.0160833
## [1223,] 1.0038274 1.0038853
## [1224,] 1.0094970 1.0095000
## [1225,] 1.0052154 1.0052692
## [1226,] 1.0019724 1.0019724
## [1227,] 1.0000006 1.0000052
## [1228,] 1.0062905 1.0083111
## [1229,] 1.0032720 1.0067555
## [1230,] 1.0061808 1.0158086
## [1231,] 1.0089813 1.0256415
## [1232,] 1.0038317 1.0080557
## [1233,] 1.0004058 1.0016564
## [1234,] 1.0065738 1.0084582
## [1235,] 1.0004746 1.0007777
## [1236,] 1.0032612 1.0041867
## [1237,] 1.0103640 1.0108970
## [1238,] 1.0035528 1.0100004
## [1239,] 1.0029685 1.0062411
## [1240,] 1.0023551 1.0074587
## [1241,] 1.0013529 1.0065937
## [1242,] 1.0051429 1.0125772
## [1243,] 1.0387120 1.0415780
## [1244,] 1.0091829 1.0140580
## [1245,] 1.0092109 1.0152383
## [1246,] 1.0444687 1.0469541
## [1247,] 1.0292182 1.0309179
## [1248,] 1.0293951 1.0302699
## [1249,] 1.0000242 1.0001549
## [1250,] 0.9999809 1.0000158
## [1251,] 1.0012237 1.0012383
## [1252,] 1.0098979 1.0118622
## [1253,] 1.0048646 1.0055660
## [1254,] 1.0014002 1.0014817
## [1255,] 1.0186157 1.0187637
## [1256,] 1.0061386 1.0068880
## [1257,] 1.0020687 1.0032932
## [1258,] 1.0071229 1.0098229
## [1259,] 1.0059421 1.0092544
## [1260,] 1.0010661 1.0047756
## [1261,] 1.0199816 1.0207783
## [1262,] 1.0035832 1.0037893
## [1263,] 1.0071950 1.0104589
## [1264,] 1.0009108 1.0015006
## [1265,] 1.0021898 1.0049086
## [1266,] 1.0158934 1.0200088
## [1267,] 1.0047864 1.0060798
## [1268,] 1.0293856 1.0342589
## [1269,] 1.0006165 1.0014287
## [1270,] 1.0021492 1.0023304
## [1271,] 1.0072822 1.0123743
## [1272,] 1.0093936 1.0173730
## [1273,] 1.0078435 1.0139600
## [1274,] 1.0011577 1.0023082
## [1275,] 1.0013708 1.0021491
## [1276,] 1.0224398 1.0245195
## [1277,] 1.0250770 1.0321363
## [1278,] 1.0030856 1.0073150
## [1279,] 1.0080412 1.0117323
## [1280,] 1.0009205 1.0038898
## [1281,] 1.0073296 1.0104092
## [1282,] 1.0026042 1.0041489
## [1283,] 1.0004258 1.0007879
## [1284,] 1.0148897 1.0157087
## [1285,] 1.0074582 1.0091934
## [1286,] 1.0000739 1.0003299
## [1287,] 1.0030194 1.0031481
## [1288,] 1.0125576 1.0130327
## [1289,] 1.0014472 1.0015430
## [1290,] 1.0046264 1.0046460
## [1291,] 1.0010402 1.0010406
## [1292,] 1.0002440 1.0007102
## [1293,] 1.0112104 1.0154995
## [1294,] 1.0008712 1.0023385
## [1295,] 1.0159495 1.0192128
## [1296,] 1.0120209 1.0143923
## [1297,] 1.0271900 1.0272663
## [1298,] 1.0010392 1.0018385
## [1299,] 1.0320561 1.0354193
## [1300,] 1.0201694 1.0205809
## [1301,] 1.0038439 1.0038497
## [1302,] 1.0017902 1.0030165
## [1303,] 1.0751791 1.0784766
## [1304,] 1.0012364 1.0059151
## [1305,] 1.0010813 1.0053715
## [1306,] 1.0009553 1.0047943
## [1307,] 1.0010902 1.0036634
## [1308,] 1.0015199 1.0040770
## [1309,] 1.0124310 1.0417545
## [1310,] 1.0004752 1.0007306
## [1311,] 1.0006199 1.0031007
## [1312,] 1.0009878 1.0025962
## [1313,] 1.0010830 1.0050446
## [1314,] 1.0022770 1.0082710
## [1315,] 1.0034092 1.0124050
## [1316,] 1.0083535 1.0316761
## [1317,] 1.0115596 1.0367574
## [1318,] 1.0089101 1.0309539
## [1319,] 1.0019072 1.0089600
## [1320,] 0.9999955 1.0000600
## [1321,] 1.0024047 1.0036323
## [1322,] 1.0067207 1.0101237
## [1323,] 1.0116420 1.0377677
## [1324,] 1.0042660 1.0099317
## [1325,] 1.0152818 1.0180519
## [1326,] 1.0064270 1.0096362
## [1327,] 1.0053759 1.0150628
## [1328,] 1.0132975 1.0259363
## [1329,] 1.0030003 1.0079433
## [1330,] 1.0041185 1.0076581
## [1331,] 1.0007991 1.0008750
## [1332,] 1.0001708 1.0005386
## [1333,] 1.0004169 1.0014589
## [1334,] 1.0007082 1.0037038
## [1335,] 1.0017107 1.0058523
## [1336,] 1.0003876 1.0020999
## [1337,] 1.0001610 1.0003295
## [1338,] 1.0069536 1.0169052
## [1339,] 1.0150124 1.0403082
## [1340,] 1.0181748 1.0522086
## [1341,] 1.0241587 1.0623670
## [1342,] 1.0440302 1.1199125
## [1343,] 1.0157803 1.0323599
## [1344,] 1.0053854 1.0087762
## [1345,] 1.0075689 1.0131589
## [1346,] 1.0060352 1.0158320
## [1347,] 1.0024104 1.0029077
## [1348,] 1.0008365 1.0009438
## [1349,] 0.9999663 0.9999865
## [1350,] 1.0004008 1.0017386
## [1351,] 1.0024638 1.0063481
## [1352,] 1.0038358 1.0156669
## [1353,] 1.0006866 1.0016586
## [1354,] 1.0019455 1.0072730
## [1355,] 1.0112325 1.0434588
## [1356,] 1.0142600 1.0480590
## [1357,] 1.0024725 1.0123074
## [1358,] 1.0003854 1.0012953
## [1359,] 1.0064540 1.0069964
## [1360,] 1.0526101 1.0590552
## [1361,] 1.0561227 1.0939633
## [1362,] 1.0774489 1.2209333
## [1363,] 1.0435491 1.0900823
## [1364,] 1.0267216 1.0499899
## [1365,] 1.0260941 1.0513047
## [1366,] 1.0324614 1.0749447
## [1367,] 1.0512174 1.1278971
## [1368,] 1.0536797 1.1480086
## [1369,] 1.0433242 1.1002908
## [1370,] 1.0349468 1.0857647
## [1371,] 1.0279029 1.0697698
## [1372,] 1.0191733 1.0549376
## [1373,] 1.0145829 1.0459751
## [1374,] 1.0125084 1.0488546
## [1375,] 1.0219965 1.0435019
## [1376,] 1.0079699 1.0192061
## [1377,] 1.0032079 1.0121847
## [1378,] 1.0049484 1.0178518
## [1379,] 1.0036176 1.0163926
## [1380,] 1.0051150 1.0167780
## [1381,] 1.0095934 1.0425787
## [1382,] 1.0033665 1.0142273
## [1383,] 1.0008500 1.0043727
## [1384,] 1.0016603 1.0034504
## [1385,] 1.0031114 1.0086102
## [1386,] 1.0200995 1.0597828
## [1387,] 1.0217490 1.0445894
## [1388,] 1.0007647 1.0036037
## [1389,] 1.0014238 1.0019624
## [1390,] 1.0052972 1.0064084
## [1391,] 1.0028600 1.0029023
## [1392,] 1.0061865 1.0180074
## [1393,] 1.0123423 1.0282504
## [1394,] 1.0024782 1.0067698
## [1395,] 1.0052436 1.0069433
## [1396,] 1.0039465 1.0049713
## [1397,] 1.0007030 1.0028360
## [1398,] 1.0056356 1.0201932
## [1399,] 1.0098607 1.0140799
## [1400,] 1.0059107 1.0059163
## [1401,] 1.0000036 1.0001014
## [1402,] 1.0020506 1.0020556
## [1403,] 1.0020258 1.0023679
## [1404,] 1.0007797 1.0014790
## [1405,] 1.0019457 1.0066086
## [1406,] 1.0067036 1.0180969
## [1407,] 1.0077618 1.0248372
## [1408,] 1.0076066 1.0249070
## [1409,] 1.0029449 1.0106276
## [1410,] 1.0024806 1.0070671
## [1411,] 1.0062897 1.0158907
## [1412,] 1.0044845 1.0113317
## [1413,] 1.0017637 1.0046611
## [1414,] 1.0022950 1.0036669
## [1415,] 1.0015825 1.0028897
## [1416,] 1.0044843 1.0083233
## [1417,] 1.0020723 1.0077081
## [1418,] 1.0047933 1.0143078
## [1419,] 1.0032176 1.0128665
## [1420,] 1.0008171 1.0038451
## [1421,] 1.0001310 1.0001343
## [1422,] 1.0002507 1.0005334
## [1423,] 1.0002632 1.0009270
## [1424,] 1.0002946 1.0015417
## [1425,] 1.0001127 1.0005544
## [1426,] 1.0002898 1.0009983
## [1427,] 1.0003582 1.0014351
## [1428,] 1.0004881 1.0022153
## [1429,] 1.0005494 1.0021010
## [1430,] 1.0001922 1.0003337
## [1431,] 1.0010190 1.0011715
## [1432,] 1.0130053 1.0358654
## [1433,] 1.0081194 1.0175721
## [1434,] 1.0025861 1.0086887
## [1435,] 1.0025629 1.0047726
## [1436,] 1.0056925 1.0199426
## [1437,] 1.0046991 1.0229323
## [1438,] 1.0134196 1.0416579
## [1439,] 1.0070570 1.0238628
## [1440,] 1.0016211 1.0055964
## [1441,] 1.0004003 1.0015235
## [1442,] 1.0064596 1.0090502
## [1443,] 1.0035031 1.0044306
## [1444,] 1.0036362 1.0041227
## [1445,] 1.0009998 1.0011546
## [1446,] 1.0002577 1.0005333
## [1447,] 1.0001006 1.0006457
## [1448,] 1.0081346 1.0204746
## [1449,] 1.0236711 1.0637039
## [1450,] 1.0057276 1.0196951
## [1451,] 1.0064111 1.0137190
## [1452,] 1.0070340 1.0146118
## [1453,] 1.0006639 1.0021149
## [1454,] 1.0027918 1.0029229
## [1455,] 1.0020807 1.0022160
## [1456,] 1.0006364 1.0008676
## [1457,] 1.0052688 1.0054428
## [1458,] 1.0011465 1.0027386
## [1459,] 1.0006254 1.0031499
## [1460,] 1.0017205 1.0022451
## [1461,] 1.0036329 1.0036346
## [1462,] 1.0029689 1.0030795
## [1463,] 1.0041897 1.0045363
## [1464,] 1.0009615 1.0010152
## [1465,] 1.0010196 1.0010368
## [1466,] 1.0008482 1.0009720
## [1467,] 1.0059711 1.0071085
## [1468,] 1.0051707 1.0077600
## [1469,] 1.0051891 1.0107816
## [1470,] 1.0044562 1.0146019
## [1471,] 1.0004574 1.0013954
## [1472,] 1.0000208 1.0001137
## [1473,] 1.0002235 1.0002239
## [1474,] 1.0002937 1.0004980
## [1475,] 1.0003199 1.0003487
## [1476,] 1.0000115 1.0002159
## [1477,] 1.0002733 1.0012789
## [1478,] 1.0020655 1.0047844
## [1479,] 1.0032348 1.0047647
## [1480,] 1.0013261 1.0042387
## [1481,] 1.0061538 1.0181203
## [1482,] 1.0073216 1.0302263
## [1483,] 1.0049546 1.0204204
## [1484,] 1.0026997 1.0107329
## [1485,] 1.0029964 1.0084849
## [1486,] 1.0012723 1.0046794
## [1487,] 1.0001323 1.0008128
## [1488,] 1.0001986 1.0007536
## [1489,] 1.0014426 1.0058093
## [1490,] 1.0012357 1.0044655
## [1491,] 1.0020307 1.0020502
## [1492,] 1.0008042 1.0014618
## [1493,] 1.0007756 1.0036990
## [1494,] 1.0013208 1.0067053
## [1495,] 1.0045649 1.0176801
## [1496,] 1.0020221 1.0079575
## [1497,] 1.0009236 1.0041763
## [1498,] 1.0004045 1.0021878
## [1499,] 1.0009677 1.0015626
## [1500,] 1.0032101 1.0039193
## [1501,] 1.0011073 1.0029577
## [1502,] 1.0005357 1.0006405
## [1503,] 1.0008080 1.0013066
## [1504,] 1.0002291 1.0013017
## [1505,] 1.0003042 1.0010895
## [1506,] 1.0003560 1.0019455
## [1507,] 1.0010770 1.0013722
## [1508,] 1.0020198 1.0020683
## [1509,] 1.0008465 1.0010885
## [1510,] 1.0003773 1.0004005
## [1511,] 1.0012766 1.0021721
## [1512,] 1.0084785 1.0300695
## [1513,] 1.0037201 1.0060277
## [1514,] 1.0015331 1.0017179
## [1515,] 1.0000411 1.0000582
## [1516,] 1.0003963 1.0020476
## [1517,] 1.0011025 1.0046266
## [1518,] 1.0014989 1.0038523
## [1519,] 1.0036541 1.0040434
## [1520,] 1.0048960 1.0053783
## [1521,] 1.0038612 1.0049532
## [1522,] 1.0001710 1.0001852
## [1523,] 1.0051155 1.0060722
## [1524,] 1.0042851 1.0046556
## [1525,] 1.0028255 1.0033136
## [1526,] 1.0018332 1.0021484
## [1527,] 1.0099517 1.0186394
## [1528,] 1.0072391 1.0330757
## [1529,] 1.0167212 1.0773403
## [1530,] 1.0157644 1.0733416
## [1531,] 1.0178089 1.0812216
## [1532,] 1.0112518 1.0534983
## [1533,] 1.0062279 1.0293967
## [1534,] 1.0077855 1.0365736
## [1535,] 1.0092875 1.0365377
## [1536,] 1.0082040 1.0334426
## [1537,] 1.0033634 1.0166736
## [1538,] 1.0017474 1.0073414
## [1539,] 1.0046076 1.0092882
## [1540,] 1.0046851 1.0133392
## [1541,] 1.0040572 1.0113099
## [1542,] 1.0056196 1.0171491
## [1543,] 1.0084971 1.0319502
## [1544,] 1.0220203 1.0498906
## [1545,] 1.0133713 1.0298547
## [1546,] 1.0121493 1.0270775
## [1547,] 1.0127145 1.0192911
## [1548,] 1.0137491 1.0220578
## [1549,] 1.0078867 1.0205908
## [1550,] 1.0041154 1.0140403
## [1551,] 1.0066944 1.0312788
## [1552,] 1.0089142 1.0416002
## [1553,] 1.0089434 1.0422782
## [1554,] 1.0105445 1.0501928
## [1555,] 1.0078185 1.0379576
## [1556,] 1.0090079 1.0357922
## [1557,] 1.0186890 1.0476881
## [1558,] 1.0231150 1.0589101
## [1559,] 1.0205552 1.0600814
## [1560,] 1.0294815 1.0764042
## [1561,] 1.0230811 1.0964784
## [1562,] 1.0325253 1.1430524
## [1563,] 1.0349130 1.1515401
## [1564,] 1.0367633 1.1596729
## [1565,] 1.0430885 1.1824172
## [1566,] 1.0451022 1.1902685
## [1567,] 1.0478751 1.2014787
## [1568,] 1.0453730 1.1922569
## [1569,] 1.0481610 1.2024169
## [1570,] 1.0437939 1.1864507
## [1571,] 1.0724459 1.2878592
## [1572,] 1.0785161 1.3041578
## [1573,] 1.0805044 1.3075764
## [1574,] 1.0752800 1.2860799
## [1575,] 1.0584181 1.2358009
## [1576,] 1.0474901 1.1962452
## [1577,] 1.0432839 1.1749674
## [1578,] 1.0290107 1.1009801
## [1579,] 1.0312768 1.0431481
## [1580,] 1.0389298 1.0398611
## [1581,] 1.0399837 1.0401304
## [1582,] 1.0033104 1.0050690
## [1583,] 1.0090610 1.0157736
## [1584,] 1.0132673 1.0267813
## [1585,] 1.0171076 1.0338064
## [1586,] 1.0410042 1.0473320
## [1587,] 1.0060153 1.0176180
## [1588,] 1.0223366 1.0435558
## [1589,] 1.0166066 1.0351062
## [1590,] 1.0075018 1.0248159
## [1591,] 1.0226489 1.0408667
## [1592,] 1.0282678 1.0536121
## [1593,] 1.0224991 1.0559541
## [1594,] 1.0271374 1.0681647
## [1595,] 1.0187255 1.0666134
## [1596,] 1.0169462 1.0647199
## [1597,] 1.0162456 1.0616165
## [1598,] 1.0170646 1.0605096
## [1599,] 1.0240876 1.0809942
## [1600,] 1.0198450 1.0784613
## [1601,] 1.0382771 1.0835402
## [1602,] 1.1556058 1.1854873
## [1603,] 1.0199880 1.0621869
## [1604,] 1.0234501 1.0855767
## [1605,] 1.0294708 1.1294180
## [1606,] 1.0353888 1.1526109
## [1607,] 1.0372282 1.1574638
## [1608,] 1.0360528 1.1545331
## [1609,] 1.0385075 1.1657260
## [1610,] 1.0380584 1.1647173
## [1611,] 1.0363966 1.1583838
## [1612,] 1.0490835 1.2026012
## [1613,] 1.0536670 1.2152838
## [1614,] 1.0539740 1.2160084
## [1615,] 1.0435554 1.1828412
## [1616,] 1.0325598 1.1415656
## [1617,] 1.0401664 1.1725475
## [1618,] 1.0290495 1.1294307
## [1619,] 1.0165048 1.0735279
## [1620,] 1.0149092 1.0457412
## [1621,] 1.0174950 1.0369331
## [1622,] 1.0115189 1.0328729
## [1623,] 1.0376515 1.0394004
## [1624,] 1.0429131 1.0489151
## [1625,] 1.0627960 1.0987680
## [1626,] 1.0770803 1.1465006
## [1627,] 1.0729787 1.1526744
## [1628,] 1.0673244 1.1576212
## [1629,] 1.0515203 1.1313290
## [1630,] 1.0300953 1.0883303
## [1631,] 1.0235641 1.0718700
## [1632,] 1.0167181 1.0499801
## [1633,] 1.0237603 1.0789476
## [1634,] 1.0167811 1.0463938
## [1635,] 1.0144673 1.0270121
## [1636,] 1.0101395 1.0109923
## [1637,] 1.0107949 1.0114847
## [1638,] 1.0100914 1.0133880
## [1639,] 1.0133023 1.0201405
## [1640,] 1.0098785 1.0321292
## [1641,] 1.0117234 1.0439214
## [1642,] 1.0130768 1.0362910
## [1643,] 1.0432418 1.0433533
## [1644,] 1.0574307 1.0596921
## [1645,] 1.0530935 1.0547885
## [1646,] 1.0222869 1.0240378
## [1647,] 1.0322525 1.0326052
## [1648,] 1.0291118 1.0291120
## [1649,] 1.0144151 1.0184892
## [1650,] 1.0151144 1.0508399
## [1651,] 1.0171483 1.0684008
## [1652,] 1.0206115 1.0786670
## [1653,] 1.0133528 1.0488329
## [1654,] 1.0263522 1.0327159
## [1655,] 1.0451775 1.0456306
## [1656,] 1.0583448 1.0644370
## [1657,] 1.0469038 1.0513058
## [1658,] 1.0195756 1.0211509
## [1659,] 1.0084332 1.0394178
## [1660,] 1.0074314 1.0267106
## [1661,] 1.0086508 1.0150030
## [1662,] 1.0222010 1.0222416
## [1663,] 1.0209692 1.0211894
## [1664,] 1.0101464 1.0140591
## [1665,] 1.0119003 1.0187615
## [1666,] 1.0171033 1.0407939
## [1667,] 1.0271252 1.0476024
## [1668,] 1.0281276 1.0646294
## [1669,] 1.0224272 1.0624909
## [1670,] 1.0240763 1.0818544
## [1671,] 1.0203665 1.0831523
## [1672,] 1.0176959 1.0655664
## [1673,] 1.0160532 1.0475415
## [1674,] 1.0130534 1.0441188
## [1675,] 1.0193229 1.0366763
## [1676,] 1.0336316 1.0374375
## [1677,] 1.0323017 1.0354108
## [1678,] 1.0385856 1.0389246
## [1679,] 1.0419508 1.0423148
## [1680,] 1.0590195 1.0629398
## [1681,] 1.0685865 1.0774894
## [1682,] 1.0714777 1.0895349
## [1683,] 1.0606473 1.0718680
## [1684,] 1.0392802 1.0397444
## [1685,] 1.0081966 1.0237007
## [1686,] 1.0076894 1.0269588
## [1687,] 1.0159654 1.0536109
## [1688,] 1.0109385 1.0421829
## [1689,] 1.0135292 1.0619372
## [1690,] 1.0101939 1.0489207
## [1691,] 1.0092531 1.0338266
## [1692,] 1.0096698 1.0209118
## [1693,] 1.0160142 1.0206325
## [1694,] 1.0160783 1.0219480
## [1695,] 1.0098781 1.0179586
## [1696,] 1.0091000 1.0121293
## [1697,] 1.0060114 1.0084184
## [1698,] 1.0053203 1.0115801
## [1699,] 1.0319010 1.0362823
## [1700,] 1.0138509 1.0161983
## [1701,] 1.0071556 1.0108288
## [1702,] 1.0123590 1.0126389
## [1703,] 1.0242299 1.0349860
## [1704,] 1.0284170 1.0514011
## [1705,] 1.0465405 1.1013100
## [1706,] 1.0358071 1.0870803
## [1707,] 1.0309219 1.0927847
## [1708,] 1.0242867 1.0860036
## [1709,] 1.0104751 1.0492062
## [1710,] 1.0300593 1.1050578
## [1711,] 1.0527622 1.1730426
## [1712,] 1.0494078 1.1619588
## [1713,] 1.0470836 1.1601613
## [1714,] 1.0324875 1.1261876
## [1715,] 1.0182053 1.0835749
## [1716,] 1.0248256 1.0988246
## [1717,] 1.0215553 1.0867002
## [1718,] 1.0108593 1.0456853
## [1719,] 1.0144261 1.0510553
## [1720,] 1.0233064 1.0766043
## [1721,] 1.0234003 1.0808497
## [1722,] 1.0416881 1.1143893
## [1723,] 1.0502443 1.1299590
## [1724,] 1.0408153 1.1121134
## [1725,] 1.0615986 1.1581110
## [1726,] 1.0703541 1.1719840
## [1727,] 1.0547559 1.1356072
## [1728,] 1.0274308 1.0833774
## [1729,] 1.0066176 1.0261654
## [1730,] 1.0022583 1.0032384
## [1731,] 1.0036650 1.0141965
## [1732,] 1.0132343 1.0421207
## [1733,] 1.0214702 1.0559645
## [1734,] 1.0342477 1.0833492
## [1735,] 1.0451607 1.0936145
## [1736,] 1.0499938 1.0986298
## [1737,] 1.0655276 1.1215736
## [1738,] 1.0578837 1.0939864
## [1739,] 1.0615580 1.0920110
## [1740,] 1.0438557 1.0540104
## [1741,] 1.0621558 1.0819111
## [1742,] 1.0585130 1.0762241
## [1743,] 1.0687381 1.0951182
## [1744,] 1.0736223 1.1023608
## [1745,] 1.0024524 1.0087125
## [1746,] 1.0018421 1.0064177
## [1747,] 1.0035852 1.0171213
## [1748,] 1.0062874 1.0307710
## [1749,] 1.0054053 1.0264466
## [1750,] 1.0036427 1.0147294
## [1751,] 1.0021753 1.0064083
## [1752,] 1.0014748 1.0032082
## [1753,] 1.0010009 1.0029565
## [1754,] 1.0011678 1.0020853
## [1755,] 1.0015943 1.0028243
## [1756,] 1.0060692 1.0061127
## [1757,] 1.0058562 1.0087387
## [1758,] 1.0034079 1.0046831
## [1759,] 1.0015402 1.0017790
## [1760,] 1.0033557 1.0055959
## [1761,] 1.0026325 1.0068431
## [1762,] 1.0046904 1.0163535
## [1763,] 1.0059601 1.0127548
## [1764,] 1.0029141 1.0085590
## [1765,] 1.0077001 1.0247519
## [1766,] 1.0056715 1.0174125
## [1767,] 1.0037674 1.0138394
## [1768,] 1.0020065 1.0099284
## [1769,] 1.0044888 1.0065731
## [1770,] 1.0022280 1.0026713
## [1771,] 1.0030184 1.0036700
## [1772,] 1.0037430 1.0053350
## [1773,] 1.0083001 1.0213314
## [1774,] 1.0087334 1.0339371
## [1775,] 1.0125272 1.0544406
## [1776,] 1.0111785 1.0478110
## [1777,] 1.0107139 1.0506594
## [1778,] 1.0145560 1.0622889
## [1779,] 1.0207377 1.0691130
## [1780,] 1.0253649 1.0733138
## [1781,] 1.0239955 1.0682720
## [1782,] 1.0208169 1.0564169
## [1783,] 1.0195017 1.0415134
## [1784,] 1.0258534 1.0430076
## [1785,] 1.0260503 1.0376915
## [1786,] 1.0227221 1.0276571
## [1787,] 1.0202627 1.0255509
## [1788,] 1.0183446 1.0248195
## [1789,] 1.0195925 1.0250857
## [1790,] 1.0259466 1.0430681
## [1791,] 1.0495447 1.1086905
## [1792,] 1.0363487 1.0803083
## [1793,] 1.0224860 1.0445465
## [1794,] 1.0136846 1.0266890
## [1795,] 1.0052670 1.0087269
## [1796,] 1.0025352 1.0063632
## [1797,] 1.0039819 1.0146085
## [1798,] 1.0013470 1.0064020
## [1799,] 1.0003672 1.0020014
## [1800,] 1.0003177 1.0003488
## [1801,] 1.0006065 1.0017153
## [1802,] 1.0004440 1.0021721
## [1803,] 1.0003943 1.0006449
## [1804,] 1.0014440 1.0018038
## [1805,] 1.0007769 1.0010899
## [1806,] 1.0004747 1.0008142
## [1807,] 1.0011388 1.0034282
## [1808,] 1.0019947 1.0045404
## [1809,] 1.0057512 1.0070714
## [1810,] 1.0028642 1.0030990
## [1811,] 1.0001347 1.0001401
## [1812,] 1.0010494 1.0010637
## [1813,] 1.0017211 1.0017986
## [1814,] 1.0016801 1.0022680
## [1815,] 1.0039404 1.0039853
## [1816,] 1.0010956 1.0011721
## [1817,] 1.0058304 1.0065565
## [1818,] 1.0029115 1.0035900
## [1819,] 1.0023325 1.0037463
## [1820,] 1.0005918 1.0006263
## [1821,] 1.0014767 1.0014767
## [1822,] 1.0028521 1.0031921
## [1823,] 1.0011876 1.0034116
## [1824,] 1.0014005 1.0044519
## [1825,] 1.0011212 1.0041014
## [1826,] 1.0027774 1.0030688
## [1827,] 1.0023265 1.0030089
## [1828,] 1.0006912 1.0012007
## [1829,] 1.0006723 1.0015237
## [1830,] 1.0008567 1.0037194
## [1831,] 1.0018430 1.0081369
## [1832,] 1.0017970 1.0087477
## [1833,] 1.0014365 1.0066928
## [1834,] 1.0012497 1.0017299
## [1835,] 1.0010437 1.0053644
## [1836,] 1.0009786 1.0050447
## [1837,] 1.0040772 1.0199979
## [1838,] 1.0061439 1.0298840
## [1839,] 1.0122441 1.0551143
## [1840,] 1.0130565 1.0596227
## [1841,] 1.0199674 1.0874986
## [1842,] 1.0223665 1.0962560
## [1843,] 1.0191816 1.0830340
## [1844,] 1.0119348 1.0550961
## [1845,] 1.0055541 1.0271645
## [1846,] 1.0032534 1.0143236
## [1847,] 1.0037986 1.0110973
## [1848,] 1.0030038 1.0039972
## [1849,] 1.0054710 1.0105414
## [1850,] 1.0104283 1.0351092
## [1851,] 1.0060680 1.0156024
## [1852,] 1.0026230 1.0079559
## [1853,] 1.0006628 1.0007856
## [1854,] 1.0006015 1.0016481
## [1855,] 1.0015413 1.0032834
## [1856,] 1.0019472 1.0030292
## [1857,] 1.0009472 1.0010359
## [1858,] 1.0013805 1.0014029
## [1859,] 1.0009068 1.0010927
## [1860,] 1.0015797 1.0057913
## [1861,] 1.0053700 1.0257516
## [1862,] 1.0078537 1.0351154
## [1863,] 1.0099074 1.0449662
## [1864,] 1.0077936 1.0373143
## [1865,] 1.0092412 1.0427810
## [1866,] 1.0102199 1.0476685
## [1867,] 1.0092151 1.0443840
## [1868,] 1.0128351 1.0597561
## [1869,] 1.0050100 1.0245218
## [1870,] 1.0012578 1.0018165
## [1871,] 1.0018214 1.0080208
## [1872,] 1.0020383 1.0102831
## [1873,] 1.0028053 1.0140492
## [1874,] 1.0012194 1.0057526
## [1875,] 1.0019172 1.0061643
## [1876,] 1.0023500 1.0095250
## [1877,] 1.0039583 1.0110055
## [1878,] 1.0035396 1.0154109
## [1879,] 1.0032445 1.0156529
## [1880,] 1.0024029 1.0106637
## [1881,] 1.0028614 1.0112004
## [1882,] 1.0022986 1.0105100
## [1883,] 1.0024851 1.0078882
## [1884,] 1.0023193 1.0062135
## [1885,] 1.0030877 1.0034601
## [1886,] 1.0020378 1.0072611
## [1887,] 1.0018772 1.0036699
## [1888,] 1.0011242 1.0034225
## [1889,] 1.0000865 1.0000941
## [1890,] 1.0006135 1.0006749
## [1891,] 1.0002850 1.0003697
## [1892,] 1.0016736 1.0079092
## [1893,] 1.0022633 1.0113738
## [1894,] 1.0069920 1.0322273
## [1895,] 1.0116967 1.0532614
## [1896,] 1.0140541 1.0643797
## [1897,] 1.0175413 1.0771444
## [1898,] 1.0184164 1.0798812
## [1899,] 1.0180485 1.0789136
## [1900,] 1.0148042 1.0662377
## [1901,] 1.0091849 1.0442385
## [1902,] 1.0063405 1.0310190
## [1903,] 1.0030628 1.0147441
## [1904,] 1.0017714 1.0059857
## [1905,] 1.0028013 1.0029289
## [1906,] 1.0085576 1.0210101
## [1907,] 1.0066993 1.0164381
## [1908,] 1.0044075 1.0102303
## [1909,] 1.0016215 1.0029766
## [1910,] 1.0005382 1.0005758
## [1911,] 1.0012505 1.0013637
## [1912,] 1.0008494 1.0020783
## [1913,] 1.0018906 1.0028219
## [1914,] 1.0023012 1.0058838
## [1915,] 1.0011640 1.0021564
## [1916,] 1.0029324 1.0036144
## [1917,] 1.0024853 1.0054007
## [1918,] 1.0048127 1.0048130
## [1919,] 1.0040346 1.0130118
## [1920,] 1.0040176 1.0188978
## [1921,] 1.0032316 1.0149864
## [1922,] 1.0025853 1.0129398
## [1923,] 1.0019249 1.0093807
## [1924,] 1.0015173 1.0018949
## [1925,] 1.0059124 1.0122939
## [1926,] 1.0122424 1.0315835
## [1927,] 1.0136895 1.0345304
## [1928,] 1.0158213 1.0251159
## [1929,] 1.0099927 1.0158493
## [1930,] 1.0105155 1.0227502
## [1931,] 1.0159734 1.0470493
## [1932,] 1.0202140 1.0641674
## [1933,] 1.0211969 1.0740518
## [1934,] 1.0129128 1.0388576
## [1935,] 1.0136048 1.0349184
## [1936,] 1.0113161 1.0303002
## [1937,] 1.0093043 1.0149430
## [1938,] 1.0091115 1.0123752
## [1939,] 1.0085694 1.0139147
## [1940,] 1.0038028 1.0039524
## [1941,] 1.0021705 1.0026663
## [1942,] 1.0024306 1.0024348
## [1943,] 1.0015892 1.0024033
## [1944,] 1.0016278 1.0029406
## [1945,] 1.0045759 1.0046341
## [1946,] 1.0064515 1.0074488
## [1947,] 1.0052959 1.0111945
## [1948,] 1.0036047 1.0103461
## [1949,] 1.0049145 1.0128769
## [1950,] 1.0040214 1.0053433
## [1951,] 1.0048518 1.0049612
## [1952,] 1.0055181 1.0066427
## [1953,] 1.0051037 1.0064781
## [1954,] 1.0027941 1.0030314
## [1955,] 1.0011220 1.0022963
## [1956,] 1.0019028 1.0064580
## [1957,] 1.0041210 1.0143300
## [1958,] 1.0036962 1.0134516
## [1959,] 1.0045900 1.0217728
## [1960,] 1.0048213 1.0231197
## [1961,] 1.0060315 1.0276366
## [1962,] 1.0033671 1.0160139
## [1963,] 1.0062606 1.0288766
## [1964,] 1.0018817 1.0046769
## [1965,] 1.0016599 1.0062535
## [1966,] 1.0036962 1.0172526
## [1967,] 1.0051336 1.0252633
## [1968,] 1.0021969 1.0074617
## [1969,] 1.0005121 1.0014764
## [1970,] 1.0008150 1.0039082
## [1971,] 1.0010504 1.0051887
## [1972,] 1.0003453 1.0012553
## [1973,] 1.0003634 1.0019136
## [1974,] 1.0058534 1.0266261
## [1975,] 1.0175471 1.0757692
## [1976,] 1.0150598 1.0693983
## [1977,] 1.0273220 1.1215619
## [1978,] 1.0169149 1.0772288
## [1979,] 1.0130026 1.0611300
## [1980,] 1.0223513 1.1001653
## [1981,] 1.0247554 1.1101432
## [1982,] 1.0224020 1.0997719
## [1983,] 1.0313296 1.1307935
## [1984,] 1.0192048 1.0846616
## [1985,] 1.0127460 1.0571345
## [1986,] 1.0115810 1.0449861
## [1987,] 1.0014742 1.0065771
## [1988,] 1.0000047 1.0001847
## [1989,] 1.0000210 1.0001736
## [1990,] 1.0003136 1.0007244
## [1991,] 1.0081005 1.0346983
## [1992,] 1.0260955 1.1124315
## [1993,] 1.0541037 1.2152884
## [1994,] 1.0588133 1.2314627
## [1995,] 1.0613797 1.2348815
## [1996,] 1.0702725 1.2597755
## [1997,] 1.0367653 1.1375236
## [1998,] 1.0230359 1.0782013
## [1999,] 1.0147185 1.0555091
## [2000,] 1.0087073 1.0338599
## [2001,] 1.0002443 1.0013627
## [2002,] 1.0002659 1.0011491
## [2003,] 1.0008757 1.0045224
## [2004,] 1.0012308 1.0055097
## [2005,] 1.0005868 1.0029453
## [2006,] 1.0011648 1.0028191
## [2007,] 1.0012461 1.0061529
## [2008,] 1.0028422 1.0131686
## [2009,] 1.0000657 1.0003842
## [2010,] 1.0001093 1.0006857
## [2011,] 1.0000134 1.0001150
## [2012,] 1.0008447 1.0015909
## [2013,] 1.0001118 1.0001157
## [2014,] 1.0016465 1.0072230
## [2015,] 1.0198317 1.0846568
## [2016,] 1.0451301 1.1766284
## [2017,] 1.0176315 1.0797945
## [2018,] 1.0068542 1.0252045
## [2019,] 1.0059057 1.0173299
## [2020,] 1.0126609 1.0389411
## [2021,] 1.0216739 1.0752342
## [2022,] 1.0281942 1.1057420
## [2023,] 1.0182143 1.0699269
## [2024,] 1.0262876 1.0912649
## [2025,] 1.0420166 1.1341523
## [2026,] 1.0365066 1.1217603
## [2027,] 1.0324355 1.0969973
## [2028,] 1.0314240 1.0963467
## [2029,] 1.0192881 1.0588437
## [2030,] 1.0167647 1.0502550
## [2031,] 1.0140447 1.0398997
## [2032,] 1.0150684 1.0455826
## [2033,] 1.0190551 1.0523400
## [2034,] 1.0222341 1.0592783
## [2035,] 1.0278825 1.0773900
## [2036,] 1.0184205 1.0441423
## [2037,] 1.0130857 1.0241548
## [2038,] 1.0111114 1.0254774
## [2039,] 1.0187930 1.0548153
## [2040,] 1.0241030 1.0829005
## [2041,] 1.0135724 1.0388828
## [2042,] 1.0069030 1.0142111
## [2043,] 1.0085667 1.0141892
## [2044,] 1.0115342 1.0268096
## [2045,] 1.0179308 1.0428483
## [2046,] 1.0237088 1.0684926
## [2047,] 1.0221290 1.0691784
## [2048,] 1.0145278 1.0348934
## [2049,] 1.0038430 1.0073750
## [2050,] 1.0045052 1.0094943
## [2051,] 1.0098086 1.0228126
## [2052,] 1.0194030 1.0640818
## [2053,] 1.0059507 1.0156602
## [2054,] 0.9999970 1.0000448
## [2055,] 1.0038743 1.0175107
## [2056,] 1.0089839 1.0367254
## [2057,] 1.0175196 1.0726086
## [2058,] 1.0161007 1.0687732
## [2059,] 1.0372007 1.1486654
## [2060,] 1.0476130 1.1849965
## [2061,] 1.0538153 1.2057824
## [2062,] 1.0488290 1.1908560
## [2063,] 1.0425578 1.1673000
## [2064,] 1.0320795 1.1291865
## [2065,] 1.0231353 1.0924509
## [2066,] 1.0083579 1.0340382
## [2067,] 1.0006067 1.0023159
## [2068,] 1.0026394 1.0127820
## [2069,] 1.0007309 1.0022125
## [2070,] 1.0022654 1.0084513
## [2071,] 1.0005781 1.0012050
## [2072,] 1.0001006 1.0002018
## [2073,] 1.0005871 1.0021949
## [2074,] 1.0002025 1.0002072
## [2075,] 1.0006374 1.0014559
## [2076,] 1.0009602 1.0023511
## [2077,] 1.0001261 1.0001625
## [2078,] 1.0019716 1.0089838
## [2079,] 1.0167096 1.0698296
## [2080,] 1.0255412 1.1021691
## [2081,] 1.0261963 1.1066322
## [2082,] 1.0143166 1.0630510
## [2083,] 1.0163976 1.0727246
## [2084,] 1.0172259 1.0743257
## [2085,] 1.0085316 1.0387087
## [2086,] 1.0025467 1.0109207
## [2087,] 1.0001580 1.0006482
## [2088,] 1.0053374 1.0213402
## [2089,] 1.0002508 1.0014172
## [2090,] 1.0037650 1.0175452
## [2091,] 1.0091998 1.0412238
## [2092,] 1.0093070 1.0408738
## [2093,] 1.0068772 1.0331712
## [2094,] 1.0033543 1.0163101
## [2095,] 1.0014993 1.0020861
## [2096,] 1.0019906 1.0092711
## [2097,] 1.0032387 1.0161302
## [2098,] 1.0047012 1.0230804
## [2099,] 1.0045955 1.0218744
## [2100,] 1.0017604 1.0078014
## [2101,] 1.0010978 1.0020960
## [2102,] 1.0026184 1.0106728
## [2103,] 1.0252697 1.1098142
## [2104,] 1.0316729 1.1289393
## [2105,] 1.0170024 1.0709371
## [2106,] 1.0197940 1.0776391
## [2107,] 1.0056502 1.0220616
## [2108,] 1.0007229 1.0027378
## [2109,] 1.0000342 1.0001961
## [2110,] 1.0006893 1.0034885
## [2111,] 1.0062272 1.0250085
## [2112,] 1.0195512 1.0759303
## [2113,] 1.0269678 1.1066782
## [2114,] 1.0355614 1.1383847
## [2115,] 1.0377936 1.1480044
## [2116,] 1.0469459 1.1798791
## [2117,] 1.0502332 1.1905907
## [2118,] 1.0504436 1.1897898
## [2119,] 1.0371512 1.1403178
## [2120,] 1.0197871 1.0826290
## [2121,] 1.0033086 1.0156702
## [2122,] 1.0004138 1.0011568
## [2123,] 1.0074630 1.0256470
## [2124,] 1.0400803 1.1385383
## [2125,] 1.0236088 1.0793562
## [2126,] 1.0078625 1.0268054
## [2127,] 1.0005576 1.0026283
## [2128,] 1.0002591 1.0013198
## [2129,] 1.0010876 1.0054903
## [2130,] 1.0011252 1.0055423
## [2131,] 1.0002334 1.0010578
## [2132,] 1.0014141 1.0072102
## [2133,] 1.0006252 1.0024848
## [2134,] 1.0000388 1.0000389
## [2135,] 1.0010480 1.0017012
## [2136,] 1.0115598 1.0308497
## [2137,] 1.0017504 1.0036366
## [2138,] 1.0049558 1.0242297
## [2139,] 1.0113132 1.0491161
## [2140,] 1.0130669 1.0559146
## [2141,] 1.0161372 1.0692020
## [2142,] 1.0067656 1.0320702
## [2143,] 1.0014382 1.0073264
## [2144,] 1.0003528 1.0011340
## [2145,] 1.0011481 1.0025584
## [2146,] 1.0007200 1.0037611
## [2147,] 1.0039314 1.0188438
## [2148,] 1.0024875 1.0120479
## [2149,] 1.0011601 1.0046261
## [2150,] 1.0001878 1.0011012
## [2151,] 1.0005773 1.0017366
## [2152,] 1.0003190 1.0004301
## [2153,] 1.0012289 1.0017051
## [2154,] 1.0032713 1.0095198
## [2155,] 1.0008098 1.0011171
## [2156,] 1.0013146 1.0056396
## [2157,] 1.0013700 1.0067352
## [2158,] 1.0092595 1.0408292
## [2159,] 1.0142986 1.0610775
## [2160,] 1.0103796 1.0412362
## [2161,] 1.0199497 1.0784208
## [2162,] 1.0251137 1.0959683
## [2163,] 1.0133982 1.0566506
## [2164,] 1.0021299 1.0107382
## [2165,] 1.0037662 1.0075909
## [2166,] 1.0163659 1.0546130
## [2167,] 1.0053259 1.0138182
## [2168,] 1.0004540 1.0020842
## [2169,] 1.0042403 1.0209939
## [2170,] 1.0058062 1.0273526
## [2171,] 1.0116195 1.0462058
## [2172,] 1.0148780 1.0596062
## [2173,] 1.0243989 1.0979320
## [2174,] 1.0249217 1.1025087
## [2175,] 1.0284231 1.1187356
## [2176,] 1.0192994 1.0856796
## [2177,] 1.0304987 1.1264016
## [2178,] 1.0301960 1.1235674
## [2179,] 1.0372375 1.1445308
## [2180,] 1.0304611 1.1157308
##
## $mpsrf
## [1] 1.495861
## parametro variable value
## 1 1 gelman 1.001433
## 2 2 gelman 1.001451
## 3 3 gelman 1.001453
## 4 4 gelman 1.001473
## 5 5 gelman 1.001477
## 6 6 gelman 1.001587
Fiz previsão \(nf = 1, 6, 12, 24\) passos à frente.
O funcionamento do algoritmo the previsão é o seguinte:
thinfac observações (aqui usei uma em 4);fc.ydraws é um objeto de dimensão [5 \times nf \times 25.000] (5 variáveis no var, nf é o número de períodos previsto e 25.000 são o número de observações que eu guardo das 100.000 simulações). Por exemplo, fc.ydraws[1,3,] contém todas as repetições da primeira variável do VAR, 3 períodos à frente;fc.mdraws contém as médias (que que é isso?) condicionais aos parâmetrs. Seu tamanho é o mesmo de fc.ydraws;fc.vdraws contém as variâncias previstas, \(V_{T+j}^{(\ell)}\) e tem tamanho \([0.5\cdot 5 \cdot (5+1) \times nf \times 25000]\). Por exemplo, fc.vdraws[,1,1] contém os elementos empilhados de \(V_{T+1}^{(1)}\) e é a primeira amostra das matriz de variância e covariância para todas variáveis, um período à frente.A primeira coisa é implementar uma função para calcular o MASE (mean absolute scaled error). Defina o termo de erro de um passo à frente como \(e_t = y_t - \hat{y}_t\). Então, podemos definir um erro padronizado como
\[q_t = \frac{e_t}{\frac{1}{n-1}\sum\limits_{i=2}^n |y_i - y_{i-1}|},\] que é independente da escala dos dados das séries. Então, o erro absoluto padronizado médio (algumas pessoas traduzem como escalado ou escalar, eu achei feio demais) é definido por
\[\text{MASE} = \text{média }(|q_t|)\]
Além desse, vou calcular também outras 2 medidas comuns, MAPE (erro médio percentual absoluto) e o MSE (erro quadrático médio). Esses estão implementados no R dentro do pacote DescTools.
Então vou fazer umas funções auxiliares para calcular o MASE e também para juntar os resultados em uma tabelinha.
# O denominador do MASE é fixo, então vou calcular ele separadamente
# Como eu junto todas as variáveis do VAR no objeto var1, vou aplicar a função sobre as colunas do var1
den_MASE <- function(serie){
n <- length(serie)
soma <- vector()
for (i in 2:n){
soma[i-1] <- abs(serie[i] - serie[i-1])
}
x <- sum(soma)/(n-1)
x
}
~Posso usar o que eu já tinha estimado.~ Não posso usar o que eu tinha estimado porque eu não separei o pedaço da amostra que vai ficar de comparação.
rm(fit1)
# Previsão
#Inflação - Produto - Juros - Câmbio - Desigualdade.
var1 <- cbind(capital_trabalho_final*100, ipca, PIB*100, swap, cambio) # The bvar function does not allows data.frames
#var2 <- cbind(capital_trabalho_final, swap, PIB2, cambio, ipca) # The bvar function does not allows data.frames
names(var1) <- c("capital_trabalho", "ipca", "pib", "swap", "cambio")
#names(var1) <- c("ipca", "pib", "swap", "cambio","capital_trabalho") # Ficou uma merda
#var1 <- c(1,2,3,4,5)
pos_ct <- grep("capital_trabalho", names(var1))
pos_swap <- grep("swap", names(var1))
pos_pib <- grep("pib", names(var1))
pos_cambio <- grep("cambio", names(var1))
pos_ipca <- grep("ipca", names(var1))
nburn. <- 1000000 # Burn the first 100kk replications
nrep. <- 100000 # Estimate another 100k times after burn in
thinfac. <- 4 # But keep only 1 in 4 estimates
p. <- 1 # Number of lags
tau. <- 48 - p. # Number of observations to use as prior
nf. <- 1 # Number of forecast periods
k_B. <- 6 # Fator de inflação na priori
k_A. <- 4 # Fator de inflação na priori
# No idea what's this for
tamanho <- floor(1/thinfac.*nrep.)
# número de tempos
tempo <- nrow(var1)
# Prepara um vetor com as últimas nf. observações para deixar de fora
amostra_1 <- var1[(nrow(var1)-nf.+1):(nrow(var1)),]
var1 <- var1[1:(nrow(var1)-nf.),]
set.seed(2747)
fit1 <- readRDS("D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Testes\\fit1for.rds")
#fit1 <- bvar.sv.tvp(var1, p=p., tau = tau., nburn = nburn., nrep = nrep., nf = nf., thinfac = thinfac.)
#saveRDS(fit1, "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Testes\\fit1for.rds")
#rm(fit1)
# Primeiro eu monto um objeto só com a previsão
# Eu sei que essa coisa tem três dimensões e quero calcular a média da terceira dimensão e ficar com uma matriz
var1_prev <- apply(fit1$fc.ydraws, c(1,2), mean)
# Agora preciso calcular os erros de previsão em cada período
# nf é o número de períodos de previsão
# amostra1 é onde ficam guardados os valores que estou prevendo
# var1_prev é onde ficam guardados os valores que eu previ
amostra1 <- matrix(amostra_1, ncol=nf.)
erro_prev <- amostra1 - var1_prev
q_t <- erro_prev/apply(var1[((tau.+p.+1):nrow(var1)),], 2, FUN = den_MASE)
MASE_1 <- abs(q_t)
MAPE_1 <- vector()
MSE_1 <- vector()
for (i in 1:ncol(var1)){
MAPE_1[i] <- MAPE(x = var1_prev[i,1], ref = amostra1[i,1])
MSE_1[i] <- MSE(x = var1_prev[i,1], ref = amostra1[i,1])
}
Agora estimo um modelo VAR(1) simples para comparar
fit_simples <- VAR(var1, p=p.)
var_simples_prev <- predict(fit_simples, n.ahead = nf.)
vars_prev <- vector()
for (i in 1:ncol(var1)){
vars_prev[i] <- (var_simples_prev[[1]][[i]][1])
}
erro_simples <- amostra_1 - vars_prev
q_t <- erro_simples/apply(var1[((tau.+p.+1):nrow(var1)),], 2, FUN = den_MASE)
MASE_1_simples <- abs(q_t)
MAPE_1_simples <- vector()
MSE_1_simples <- vector()
vars_prev <- matrix(vars_prev, ncol = 1)
amostra_1 <- matrix(amostra_1, ncol = 1)
for (i in 1:ncol(var1)){
MAPE_1_simples[i] <- MAPE(x = vars_prev[i,1], ref = amostra_1[i,1])
MSE_1_simples[i] <- MSE(x = vars_prev[i,1], ref = amostra_1[i,1])
}
# Primeiro eu monto um objeto só com a previsão
# Eu sei que essa coisa tem três dimensões e quero calcular a média da terceira dimensão e ficar com uma matriz
var6_prev <- apply(fit1$fc.ydraws, c(1,2), mean)
# Agora preciso calcular os erros de previsão em cada período
# nf é o número de períodos de previsão
# amostra1 é onde ficam guardados os valores que estou prevendo
# var1_prev é onde ficam guardados os valores que eu previ
amostra6 <- t(amostra_1)
erro_prev <- amostra6 - var6_prev
q_t <- abs(erro_prev/apply(var1[((tau.+p.+1):nrow(var1)),], 2, FUN = den_MASE))
MASE_6 <- apply(q_t, 1, sum)
MAPE_6 <- vector()
MSE_6 <- vector()
for (i in 1:ncol(var1)){
MAPE_6[i] <- MAPE(x = var6_prev[i,1:nf.], ref = amostra6[i,1:nf.])
MSE_6[i] <- MSE(x = var6_prev[i,1:nf.], ref = amostra6[i,1:nf.])
}
Agora estimo um modelo VAR(1) simples para comparar
fit_simples <- VAR(var1, p=p.)
var_simples_prev <- predict(fit_simples, n.ahead = nf.)
vars_prev <- matrix(NA, ncol = ncol(var1), nrow = nf.)
for (i in 1:ncol(var1)){
vars_prev[,i] <- (var_simples_prev[[1]][[i]][,1])
}
erro_simples <- amostra_1 - vars_prev
q_t <- abs(erro_simples/apply(var1[((tau.+p.+1):nrow(var1)),], 2, FUN = den_MASE))
MASE_6_simples <- apply(q_t, 2, sum)
MAPE_6_simples <- vector()
MSE_6_simples <- vector()
for (i in 1:ncol(var1)){
MAPE_6_simples[i] <- MAPE(x = vars_prev[1:nf.,i], ref = amostra_1[1:nf.,i])
MSE_6_simples[i] <- MSE(x = vars_prev[1:nf.,i], ref = amostra_1[1:nf.,i])
}
rm(fit1)
#Inflação - Produto - Juros - Câmbio - Desigualdade.
var1 <- cbind(capital_trabalho_final*100, ipca, PIB*100, swap, cambio) # The bvar function does not allows data.frames
#var2 <- cbind(capital_trabalho_final, swap, PIB2, cambio, ipca) # The bvar function does not allows data.frames
names(var1) <- c("capital_trabalho", "ipca", "pib", "swap", "cambio")
#names(var1) <- c("ipca", "pib", "swap", "cambio","capital_trabalho") # Ficou uma merda
#var1 <- c(1,2,3,4,5)
pos_ct <- grep("capital_trabalho", names(var1))
pos_swap <- grep("swap", names(var1))
pos_pib <- grep("pib", names(var1))
pos_cambio <- grep("cambio", names(var1))
pos_ipca <- grep("ipca", names(var1))
nburn. <- 1000000 # Burn the first 100kk replications
nrep. <- 100000 # Estimate another 100k times after burn in
thinfac. <- 4 # But keep only 1 in 4 estimates
p. <- 1 # Number of lags
tau. <- 48 - p. # Number of observations to use as prior
nf. <- 12 # Number of forecast periods
k_B. <- 6 # Fator de inflação na priori
k_A. <- 4 # Fator de inflação na priori
# No idea what's this for
tamanho <- floor(1/thinfac.*nrep.)
# número de tempos
tempo <- nrow(var1)
# Prepara um vetor com as últimas nf. observações para deixar de fora
amostra_1 <- var1[(nrow(var1)-nf.+1):(nrow(var1)),]
var1 <- var1[1:(nrow(var1)-nf.),]
set.seed(2747)
fit1 <- readRDS("D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Testes\\fit12for.rds")
#fit1 <- bvar.sv.tvp(var1, p=p., tau = tau., nburn = nburn., nrep = nrep., nf = nf., thinfac = thinfac.)
#saveRDS(fit1, "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Testes\\fit12for.rds")
#rm(fit1)
# Primeiro eu monto um objeto só com a previsão
# Eu sei que essa coisa tem três dimensões e quero calcular a média da terceira dimensão e ficar com uma matriz
var12_prev <- apply(fit1$fc.ydraws, c(1,2), mean)
# Agora preciso calcular os erros de previsão em cada período
# nf é o número de períodos de previsão
# amostra1 é onde ficam guardados os valores que estou prevendo
# var1_prev é onde ficam guardados os valores que eu previ
amostra12 <- t(amostra_1)
erro_prev <- amostra12 - var12_prev
q_t <- abs(erro_prev/apply(var1[((tau.+p.+1):nrow(var1)),], 2, FUN = den_MASE))
MASE_12 <- apply(q_t, 1, sum)
MAPE_12 <- vector()
MSE_12 <- vector()
for (i in 1:ncol(var1)){
MAPE_12[i] <- MAPE(x = var12_prev[i,1:nf.], ref = amostra12[i,1:nf.])
MSE_12[i] <- MSE(x = var12_prev[i,1:nf.], ref = amostra12[i,1:nf.])
}
Agora estimo um modelo VAR(1) simples para comparar
fit_simples <- VAR(var1, p=p.)
var_simples_prev <- predict(fit_simples, n.ahead = nf.)
vars_prev <- matrix(NA, ncol = ncol(var1), nrow = nf.)
for (i in 1:ncol(var1)){
vars_prev[,i] <- (var_simples_prev[[1]][[i]][,1])
}
erro_simples <- amostra_1 - vars_prev
q_t <- abs(erro_simples/apply(var1[((tau.+p.+1):nrow(var1)),], 2, FUN = den_MASE))
MASE_12_simples <- apply(q_t, 2, sum)
MAPE_12_simples <- vector()
MSE_12_simples <- vector()
for (i in 1:ncol(var1)){
MAPE_12_simples[i] <- MAPE(x = vars_prev[1:nf.,i], ref = amostra_1[1:nf.,i])
MSE_12_simples[i] <- MSE(x = vars_prev[1:nf.,i], ref = amostra_1[1:nf.,i])
}
rm(fit1)
# Previsão
#Inflação - Produto - Juros - Câmbio - Desigualdade.
var1 <- cbind(capital_trabalho_final*100, ipca, PIB*100, swap, cambio) # The bvar function does not allows data.frames
#var2 <- cbind(capital_trabalho_final, swap, PIB2, cambio, ipca) # The bvar function does not allows data.frames
names(var1) <- c("capital_trabalho", "ipca", "pib", "swap", "cambio")
#names(var1) <- c("ipca", "pib", "swap", "cambio","capital_trabalho") # Ficou uma merda
#var1 <- c(1,2,3,4,5)
pos_ct <- grep("capital_trabalho", names(var1))
pos_swap <- grep("swap", names(var1))
pos_pib <- grep("pib", names(var1))
pos_cambio <- grep("cambio", names(var1))
pos_ipca <- grep("ipca", names(var1))
nburn. <- 1000000 # Burn the first 100kk replications
nrep. <- 100000 # Estimate another 100k times after burn in
thinfac. <- 4 # But keep only 1 in 4 estimates
p. <- 1 # Number of lags
tau. <- 48 - p. # Number of observations to use as prior
nf. <- 24 # Number of forecast periods
k_B. <- 6 # Fator de inflação na priori
k_A. <- 4 # Fator de inflação na priori
# No idea what's this for
tamanho <- floor(1/thinfac.*nrep.)
# número de tempos
tempo <- nrow(var1)
# Prepara um vetor com as últimas nf. observações para deixar de fora
amostra_1 <- var1[(nrow(var1)-nf.+1):(nrow(var1)),]
var1 <- var1[1:(nrow(var1)-nf.),]
set.seed(2747)
fit1 <- readRDS("D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Testes\\fit24for.rds")
#fit1 <- bvar.sv.tvp(var1, p=p., tau = tau., nburn = nburn., nrep = nrep., nf = nf., thinfac = thinfac.)
#saveRDS(fit1, "D:\\Onedrive - Aisha\\OneDrive\\Documentos\\Mestrado Economia\\Dissertação\\YSI - Buenos Aires\\Testes\\fit24for.rds")
#rm(fit1)
# Primeiro eu monto um objeto só com a previsão
# Eu sei que essa coisa tem três dimensões e quero calcular a média da terceira dimensão e ficar com uma matriz
var24_prev <- apply(fit1$fc.ydraws, c(1,2), mean)
# Agora preciso calcular os erros de previsão em cada período
# nf é o número de períodos de previsão
# amostra1 é onde ficam guardados os valores que estou prevendo
# var1_prev é onde ficam guardados os valores que eu previ
amostra24 <- t(amostra_1)
erro_prev <- amostra24 - var24_prev
q_t <- abs(erro_prev/apply(var1[((tau.+p.+1):nrow(var1)),], 2, FUN = den_MASE))
MASE_24 <- apply(q_t, 1, sum)
MAPE_24 <- vector()
MSE_24 <- vector()
for (i in 1:ncol(var1)){
MAPE_24[i] <- MAPE(x = var24_prev[i,1:nf.], ref = amostra24[i,1:nf.])
MSE_24[i] <- MSE(x = var24_prev[i,1:nf.], ref = amostra24[i,1:nf.])
}
Agora estimo um modelo VAR(1) simples para comparar
fit_simples <- VAR(var1, p=p.)
var_simples_prev <- predict(fit_simples, n.ahead = nf.)
vars_prev <- matrix(NA, ncol = ncol(var1), nrow = nf.)
for (i in 1:ncol(var1)){
vars_prev[,i] <- (var_simples_prev[[1]][[i]][,1])
}
erro_simples <- amostra_1 - vars_prev
q_t <- abs(erro_simples/apply(var1[((tau.+p.+1):nrow(var1)),], 2, FUN = den_MASE))
MASE_24_simples <- apply(q_t, 2, sum)
MAPE_24_simples <- vector()
MSE_24_simples <- vector()
for (i in 1:ncol(var1)){
MAPE_24_simples[i] <- MAPE(x = vars_prev[1:nf.,i], ref = amostra_1[1:nf.,i])
MSE_24_simples[i] <- MSE(x = vars_prev[1:nf.,i], ref = amostra_1[1:nf.,i])
}
Agora vamos juntar todo mundo numa tabelinha bonitinha.
matrizona <- matrix(NA, ncol = ncol(var1), nrow = (2*3*4)) # 3 measures and 4 times 2 methods
colnames(matrizona) <- c("capital trabalho", "ipca", "pib", "swap", "cambio")
rownames(matrizona) <- c("MASE TVP-VAR 1", "MASE VAR 1", "MSE TVP-VAR 1", "MSE VAR 1", "MAPE TVP-VAR 1", "MAPE VAR 1",
"MASE TVP-VAR 6", "MASE VAR 6", "MSE TVP-VAR 6", "MSE VAR 6", "MAPE TVP-VAR 6", "MAPE VAR 6",
"MASE TVP-VAR 12", "MASE VAR 12", "MSE TVP-VAR 12", "MSE VAR 12", "MAPE TVP-VAR 12", "MAPE VAR 12",
"MASE TVP-VAR 24", "MASE VAR 24", "MSE TVP-VAR 24", "MSE VAR 24", "MAPE TVP-VAR 24", "MAPE VAR 24")
matrizona[1,] <- as.vector(MASE_1)
# 1 step
matrizona[1,] <- round(as.vector(MASE_1),4)
matrizona[2,] <- round(MASE_1_simples, 4)
matrizona[3,] <- round(MSE_1, 4)
matrizona[4,] <- round(MSE_1_simples, 4)
matrizona[5,] <- round(MAPE_1, 4)
matrizona[6,] <- round(MAPE_1_simples, 4)
# 6 steps
matrizona[7,] <- round(MASE_6,4)
matrizona[8,] <- round(MASE_6_simples, 4)
matrizona[9,] <- round(MSE_6, 4)
matrizona[10,] <- round(MSE_6_simples, 4)
matrizona[11,] <- round(MAPE_6, 4)
matrizona[12,] <- round(MAPE_6_simples, 4)
# 12 steps
matrizona[13,] <- round(MASE_12,4)
matrizona[14,] <- round(MASE_12_simples, 4)
matrizona[15,] <- round(MSE_12, 4)
matrizona[16,] <- round(MSE_12_simples, 4)
matrizona[17,] <- round(MAPE_12, 4)
matrizona[18,] <- round(MAPE_12_simples, 4)
# 24 steps
matrizona[19,] <- round(MASE_24,4)
matrizona[20,] <- round(MASE_24_simples, 4)
matrizona[21,] <- round(MSE_24, 4)
matrizona[22,] <- round(MSE_24_simples, 4)
matrizona[23,] <- round(MAPE_24, 4)
matrizona[24,] <- round(MAPE_24_simples, 4)
matrizona <- data.frame(matrizona)
#stargazer(matrizona, summary=FALSE, header = TRUE, type = 'latex')
stargazer(matrizona, summary=FALSE, header = TRUE, type = 'html')
##
## <table style="text-align:center"><tr><td colspan="6" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"></td><td>capital.trabalho</td><td>ipca</td><td>pib</td><td>swap</td><td>cambio</td></tr>
## <tr><td colspan="6" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">MASE TVP-VAR 1</td><td>0.005</td><td>0.464</td><td>0.432</td><td>0.146</td><td>0.674</td></tr>
## <tr><td style="text-align:left">MASE VAR 1</td><td>0.322</td><td>0.658</td><td>0.380</td><td>1.742</td><td>0.589</td></tr>
## <tr><td style="text-align:left">MSE TVP-VAR 1</td><td>0.002</td><td>0.026</td><td>1.046</td><td>0.005</td><td>3.799</td></tr>
## <tr><td style="text-align:left">MSE VAR 1</td><td>8.819</td><td>0.052</td><td>0.809</td><td>0.684</td><td>2.902</td></tr>
## <tr><td style="text-align:left">MAPE TVP-VAR 1</td><td>0.001</td><td>0.057</td><td>4.318</td><td>0.011</td><td>0.019</td></tr>
## <tr><td style="text-align:left">MAPE VAR 1</td><td>0.060</td><td>0.080</td><td>3.797</td><td>0.126</td><td>0.017</td></tr>
## <tr><td style="text-align:left">MASE TVP-VAR 6</td><td>1.633</td><td>4.111</td><td>3.194</td><td>2.622</td><td>6.589</td></tr>
## <tr><td style="text-align:left">MASE VAR 6</td><td>10.761</td><td>3.371</td><td>7.140</td><td>24.130</td><td>4.733</td></tr>
## <tr><td style="text-align:left">MSE TVP-VAR 6</td><td>7.570</td><td>0.092</td><td>1.848</td><td>0.075</td><td>14.099</td></tr>
## <tr><td style="text-align:left">MSE VAR 6</td><td>3.108</td><td>0.194</td><td>1.812</td><td>10.248</td><td>1.203</td></tr>
## <tr><td style="text-align:left">MAPE TVP-VAR 6</td><td>0.050</td><td>0.086</td><td>1.591</td><td>0.031</td><td>0.032</td></tr>
## <tr><td style="text-align:left">MAPE VAR 6</td><td>0.030</td><td>0.133</td><td>1.548</td><td>0.441</td><td>0.009</td></tr>
## <tr><td style="text-align:left">MASE TVP-VAR 12</td><td>5.277</td><td>63.799</td><td>5.990</td><td>83.379</td><td>30.893</td></tr>
## <tr><td style="text-align:left">MASE VAR 12</td><td>33.286</td><td>27.907</td><td>16.834</td><td>71.177</td><td>56.746</td></tr>
## <tr><td style="text-align:left">MSE TVP-VAR 12</td><td>23.827</td><td>3.985</td><td>1.968</td><td>12.983</td><td>69.977</td></tr>
## <tr><td style="text-align:left">MSE VAR 12</td><td>8.854</td><td>4.103</td><td>1.958</td><td>31.123</td><td>17.903</td></tr>
## <tr><td style="text-align:left">MAPE TVP-VAR 12</td><td>0.080</td><td>0.664</td><td>1.593</td><td>0.445</td><td>0.077</td></tr>
## <tr><td style="text-align:left">MAPE VAR 12</td><td>0.050</td><td>0.673</td><td>1.504</td><td>0.690</td><td>0.039</td></tr>
## <tr><td style="text-align:left">MASE TVP-VAR 24</td><td>5.277</td><td>63.799</td><td>5.990</td><td>83.379</td><td>30.893</td></tr>
## <tr><td style="text-align:left">MASE VAR 24</td><td>33.286</td><td>27.907</td><td>16.834</td><td>71.177</td><td>56.746</td></tr>
## <tr><td style="text-align:left">MSE TVP-VAR 24</td><td>23.827</td><td>3.985</td><td>1.968</td><td>12.983</td><td>69.977</td></tr>
## <tr><td style="text-align:left">MSE VAR 24</td><td>8.854</td><td>4.103</td><td>1.958</td><td>31.123</td><td>17.903</td></tr>
## <tr><td style="text-align:left">MAPE TVP-VAR 24</td><td>0.080</td><td>0.664</td><td>1.593</td><td>0.445</td><td>0.077</td></tr>
## <tr><td style="text-align:left">MAPE VAR 24</td><td>0.050</td><td>0.673</td><td>1.504</td><td>0.690</td><td>0.039</td></tr>
## <tr><td colspan="6" style="border-bottom: 1px solid black"></td></tr></table>